burigana_jenam2004.tex
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\centerline{{\em \bf JENAM 2004 -- The many scales in the Universe}}

\vspace*{5.00 cm}

\centerline{\bf\Large{Cosmological reionization after WMAP:}} 
\vspace*{0.5 cm}
\centerline{\bf\Large{perspectives from {\sc PLANCK} and future CMB missions}}

\vspace*{2.00 cm}

\centerline{\em C.~Burigana$^1$, L.A.~Popa$^{1,2}$, F.~Finelli$^1$, 
R.~Salvaterra$^3$, G.~De~Zotti$^{4,3}$, and N.~Mandolesi$^1$} 

\vspace*{1.00 cm}

\centerline{$^1$INAF-CNR/IASF, Sezione di Bologna, via Gobetti 101, 
I-40129 Bologna (Italy)}
\centerline{$^2$Institute for Space Sciences, Bucharest-Magurele R-76900 (Romania)} 
\centerline{$^3$SISSA, via Beirut 4, I-34014 Trieste (Italy)}
\centerline{$^4$INAF - Osservatorio Astronomico di Padova, vicolo 
dell'Osservatorio 5, I-35122 Padova (Italy)}

\vspace*{1.00 cm}

%\begin{center}
%{\em Short title}\\
%{\bf Implications of future of CMB space experiments}
%\end{center}

%\newpage

\centerline{\bf Abstract} 

\vspace*{0.5cm}

\noindent 
The WMAP first year detection of a high redshift reionization through its 
imprints
on CMB anisotropy T and TE mode angular power spectra calls for a better  
comprehension of the universe ionization and thermal history after the 
standard recombination. Different reionization mechanisms predict 
different signatures in the CMB, both in temperature and polarization
anisotropies and in spectral distortions. The {\sc Planck} capability 
to distinguish among different scenarios through its sensitivity to
T, TE, and E mode angular power spectra is discussed. Perspectives 
open by future high sensitivity experiments on the CMB polarization
anisotropy and spectrum are also presented.

\section{Introduction}
\label{sec:introduction}

The accurate understanding of the ionization history of the universe
plays a fundamental role in modern cosmology.
The classical theory of hydrogen
recombination for pure baryonic cosmological models
%Peebles - Zel'dovich, Kurt and Sunyaev   
\cite{peebles, zeldovich}, 
subsequently extended to non-baryonic dark matter models 
%Zabotin and Naselsky  -  Jones and Wyse  - Seager, Sasselov and Scott -
% Peebles, Seager and Hu
\cite{zabotin, jones, recfast, psh}
can be modified in various ways to take into account
additional sources of photon and energy production
able to significantly
increase the ionization fraction, $x_e$,
above the residual fraction ($\sim10^{-3}$)
after the standard recombination epoch
at $\zrec\simeq 10^3$.
These photon and energy production processes may leave imprints
on the cosmic microwave background (CMB) providing a crucial 
``integrated'' information on the so-called
{\it dark} and {\it dawn} {\it ages}, i.e. the epochs
before or at the beginning the formation of first stars and primeval galaxies,
complementary to those obtained by the study of the diffuse backgrounds
in other frequency bands and that are impossible or difficult to 
study with other direct astronomical observations.

Among the extraordinary results recently achieved by WMAP
\cite{bennett2003}
the detection of a cosmological reionization at relevant 
redshifts 
\cite{kogutetal03}
represents one of the new most remarkable
discovery in the recent years. 
In spite of the uncertainty associated to the degeneracy
\cite{bondetal_deg} between the Thomson scattering 
optical depth, $\tau$, and 
the spectral index of primordial perturbation, $n_s$,
in CMB anisotropy data,  
a cosmological reionization at substantial 
redshifts is supported 
by the decrease of the temperature
angular power spectrum at high multipoles 
and by an excess in the
TE cross-power spectrum on large angular scale
(multipoles $\ell \lsim 7$) with respect to models
with no-reionization or reionization with quite low ($\sim 0.05$) values
of $\tau$.
According to WMAP 1-yr data, 
the favourite values of $\tau$ are $\gsim 0.1$, 
with a current best fit of $\simeq 0.17$ based on the combination of WMAP with 
additional CMB anisotropy data at higher resolution and 
other kinds of astronomical observations (see, e.g.,
\cite{PBM_NA}).
On the other hand, 
the details and the physical 
explanation of the cosmological reionization 
are still unclear. 

Since the WMAP detection of the reionization
at substantial redshifts, many models have been 
proposed and/or reconsidered to account for the measure 
of $\tau$ (see, e.g., \cite{bean}).
Certainly, a significant contribution 
($\simeq 0.05-0.07$) to the value of $\tau$ 
derives from the ionization, 
likely associated to photon production
and hot gas ejection by primeval galaxies and quasars,
at relatively low redshifts ($z \lsim \zreio^{(2)} \simeq 5-7$) 
where direct observations of the Gunn-Peterson effect
in quasars probe a high ionization level of the intergalactic medium.
The remaining contribution ($\simeq 0.05-0.12$) to the observed value 
of $\tau$ should be provided by processes at higher redshifts.
Although uncertain because of the possible non-uniformity 
of the ionization of the intergalactic medium,
the indication of an increase of the Ly-$\alpha$ opacity 
for Gunn-Peterson tests toward some quasars at $z \sim 6$
\cite{becker, fan, fan2004}
combined to the large WMAP value of $\tau$
suggests the possibility of a twice reionization, the first one
at relevant redshifts, $\zreio^{(1)}\simeq 15$, possibly associated
to Population III stars \cite{cen2003}, or even at higher redshifts,
$\zreio \gsim some \times 10$, in models involving 
a relevant photon production by particle decay, 
matter-antimatter annihilation, or black-hole evaporation
and so on, followed by the subsequent 
reionization at $z \simeq \zreio^{(2)} \simeq 6$. 

The reionization imprints on the CMB 
can be divided in three categories: $i)$ decreasing of the power
of CMB temperature anisotropy at large multipoles
because of photon diffusion, $ii)$ increasing
of the power of CMB polarization and temperature-polarization
cross correlation anisotropy at all multipoles with relevant
features possibly more remarkable at low and middle multipoles 
according to the reionization epoch
because of the delay of the effective last scattering surface, 
$iii)$ generation of CMB Comptonization and free-free spectral distortions 
associated to the heating of the electron temperature of the 
intergalactic medium during the reionization epoch.
The imprints on CMB anisotropies are mainly dependent 
on the ionization history while 
CMB spectral distortions strongly depend 
also on the thermal history. 

    \section{Observational perspectives from next and future experiments}
    \label{sec:obs_anis}

The CMB anisotropy pattern is a single
realization of a stochastic process and therefore 
it may be different from the average over the ensemble 
of all possible realizations of the given (true) cosmological model 
with given parameters. 
This translates into the fact that the $a_{\ell m}$ coefficients
are random variables (possibly following a Gaussian distribution), at a 
given $\ell$, and therefore
their variance, $C_\ell$, is $\chi^2$ distributed with $2\ell +1$ degrees of
freedom. The relative variance $\delta C_\ell$ on $C_\ell$ is equal to 
$\sqrt{2/(2\ell+1)}$ and is quite relevant at low $\ell$s.
% because of 
%the relatively small number of available modes. 
This is the so-called ``cosmic variance'' which limits the accuracy
of the comparison of observations with theoretical predictions.
%that defines the ultimate limit 
%on the accuracy at which a given cosmological model defined by
%an appropriate set of parameters can be constrained 
%by the CMB angular power spectrum.
Another similar variance in CMB anisotropy experiments 
is related to the sky coverage since the detailed CMB anisotropy 
statistical properties may depend on the considered sky patch.
This variance depends on the observed sky fraction, $f_{\rm sky}$. 
At multipoles larger than $few \times 10^2$ the most 
relevant uncertainties are related to the experiment resolution and 
sensitivity. All these terms contribute to the final uncertainty on the
$C_\ell$ according to \cite{knox}:
\begin{equation}
\frac{\delta C_\ell}{C_\ell} = \sqrt{\frac{2}{f_{\rm sky}(2\ell+1)}}\left[
1+\frac{A\sigma^2}{NC_\ell W_\ell}\right]\, ,
\label{fullvariance}
\end{equation} 
where $A$ is the size of the surveyed area, $\sigma$ is the rms noise per pixel,
$N$ is the total number of observed pixel, and $W_\ell$ is the beam window
function. For a symmetric Gaussian beam 
$W_\ell = {\rm exp}(-\ell(\ell+1)\sigma_{\rm B}^2)$ where
$\sigma_{\rm B} = {\rm FWHM}/\sqrt{8{\rm ln}2}$ 
defines the beam resolution.

The two instruments at cryogenic temperatures
on-board the ESA {\sc Planck}
satellite
%~\footnote{http://astro.estec.esa.nl/Planck}
\cite{tauber00} 
(see also J. Tauber 2004, {\it this Meeting}), 
the Low Frequency Instrument (LFI; \cite{lfi98};
see also N. Mandolesi 2004, {\it this Meeting})
based on differential radiometers  
and the High Frequency Instrument (HFI; \cite{hfi98})
based on state-of-art bolometers
at the focus of a 1.5~m aperture off-axis Gregorian telescope,
will measure the CMB angular power spectrum
with very high sensitivity up to multipoles $\ell \sim 1000-2000$
and an accurate control of the systematic effects.
The two instruments will cover a frequency range from 
30 to 857~GHz, necessary to accurately subtract the foreground
contamination (see, e.g., G. De~Zotti et al. 2004, {\it this Meeting}),
with a (FWHM) resolution from $\sim 33'$ to $5'$   
and a sensitivity from $\sim 15 \mu$K to the $\sim \mu$K level
in terms of antenna temperature on a square resolution element of with
side of $\sim 10'$. 

\begin{figure}
\vspace{-0.5cm}
\epsfig{figure=cmb_map_lfigoal_hfi_2003_bw.ps,width=15cm,height=14cm}
\caption{Comparison between {\sc Planck} and WMAP resolution and
sensitivity. For each considered frequency
channel, the crossing between the CMB convolved angular power spectrum
and the residual instrumental white noise angular power spectrum
indicates the multipole value where the signal to noise ratio
($\ell$ by $\ell$) is close to unity.
Of course, binning the power spectrum on a suitable range of multipoles,
as possible because of the smooth 
variation of $C_\ell$ with $\ell$,
will allow to recover the CMB power spectrum with a good 
accuracy also at multipoles comparable that those 
corresponding to the crossings between the noise and CMB power 
spectra reported in the figure (for example 
for the {\sc Planck} channels at 70--100~GHz 
at $\ell \sim 1500$ a $\sim 3$\% binning over $\ell$ allows to 
reduce the uncertainty on the $C_\ell$ recovery to $\sim 15$\%).}
\label{planckvsmap}
\end{figure}

Fig.~\ref{planckvsmap} compares {\sc Planck} and 
WMAP
%~\footnote{http://lambda.gsfc.nasa.gov} 
final performances
in terms of angular power spectrum recovery.
Note that, at similar frequencies, the better sensitivity of {\sc Planck}
with respect to WMAP is mainly due to the lower level of the {\sc Planck} 
instrumental noise achieved thanks to the better radiometer performance
assured by the lower system temperature while at higher frequencies
it derives from a combination of lower instrumental noise achieved thanks to 
high sensitivity bolometers and from the improving of resolution  
with the frequency for a given telescope size.
The CMB angular power spectrum is reported without beam smoothing and by taking into
account the beam window functions of several {\sc Planck} frequency
channels and of the highest WMAP frequency channel (which resolution is very close 
to that of the LFI 70~GHz channel). The corresponding angular power spectra
of the residual nominal white noise (i.e. after the subtraction of
the expectation value of the noise angular power spectrum) are also 
displayed. Similar considerations hold also for the measure of the polarization 
anisotropies (see, e.g., \cite{dsum02} for a summary of 
CMB polarization experiments). 
The sensitivity to the anisotropy measure of 
the Stokes parameters $Q$ and $U$ and of the polarization 
signal $P$ ($P=\sqrt{Q^2+U^2}$) is $\sim \sqrt{2} - 2$ times worse 
than that for the temperature anisotropy,
the exact value depending on to the detailed experimental strategy 
adopted to recover them from the combination of multi-beam 
data~\footnote{
For example, a ratio $\sqrt{2}$ can be easily obtained by taking into 
account that for differential radiometers the information from four receivers coupled to
two feeds can be combined to derive a measure of a single temperature 
anisotropy data or of two ($Q$ and $U$) polarization anisotropy data.}.
The low (of few--some~\%) polarization level predicted, and still only
approximately measured \cite{kovac2002}, for the CMB anisotropy clearly calls 
for high sensitivity measurements which are
less crucial for the temperature-polarization cross correlation
(TE-mode) already measured by WMAP.

A quite accurate measure of the E-mode polarization 
is expected from the next WMAP data release, at least at degree scales,  
while the {\sc Planck} instruments will have a good sensitivity  
to the polarization E-mode angular power spectrum also at scales
of some arcminutes, the main limitation being represented 
by the foreground contamination, 
as shown in Fig.~\ref{cl_pol_nu}.

%\begin{figure}
%\vspace{-2.cm}
\begin{figure}[t]
\vspace{-0.5cm}
\begin{center}
\epsfig{file=dt_l_100_1000_bw_sxdx1_lensing_update_shadow_rgpol5percent.ps,width=16.cm,height=14cm}
\end{center}
\vspace{-6.5cm}
\caption{Typical predicted ranges for the CMB 
polarization angular power spectra 
(E-mode, upper dotted regions; B-mode, lower dotted regions) 
including the lensing \cite{SZlensing}
compared to the 
foreground contamination (radiogalaxies (dots) contribution 
%assuming a polarization degree of 2.8\% 
(see \cite{tucci}
for a recent detailed study);
the small contribution expected from infra-red galaxies (dashes); 
Galactic dust (three dots-dashes) and 
synchrotron (dot-dashes) emission \cite{bl02, dsum02})   
at two representative multipoles, as function of the 
frequency. 
%(see also Fig.~\ref{cl_pol} and Sects.~\ref{sec:foreissue},
%\ref{sec:pol}, and \ref{sec:gravwave}). 
We report the final sensitivity of WMAP at 94~GHz 
(asterisk) and of some {\sc Planck} frequency channels (crosses) binned
over a quite large range of multipoles.
%(for {\sc Planck}, we assume a polarization sensitivity of the HFI 
%100~GHz channel, currently under implementation, similar to that 
%at 143~GHz).
}
\vspace{-0.2cm}
\label{cl_pol_nu}
\end{figure}

Thanks to the combination of temperature and polarization high quality data,
{\sc Planck} is expected to reduce the error bars in the recovery of the 
cosmological parameters at the level of
$few$~\% or better and the final accuracy 
on a wide set of cosmological parameters 
will be largely independent \cite{pbm01}
of the auxiliary information coming from
other classes of astronomical observations which will be
necessary to just remove some degeneracies intrinsic 
in the CMB information \cite{bondetal_deg}.
As an example, Fig.~3 compares the {\sc Planck}
sensitivity 
in constraining the Thomson optical depth
and the density contrast with 
the sensitivity of WMAP, possibly combined with the Ly-$\alpha$ forest 
information (from \cite{PBM_NA}).

The {\sc Planck} sensitivity and resolution will allow 
not only an extremely precise determination of the 
CMB angular power spectrum but also an accurate 
and multi-frequency imaging of the temperature anisotropy pattern 
on the whole sky and a quite accurate imaging of the polarization anisotropy
pattern at least on some sky areas of particular 
sensitivity~\footnote{
Analogously to the WMAP survey, the scanning strategies foreseen for 
{\sc Planck} will imply that the sky pixels on two areas (each of about 20--30
squared degrees) close to the ecliptic 
poles will be observed for a time significantly longer than the average 
resulting into a sensitivity significantly better 
(by about 5 times) than the average.}
by combining the multi-frequency information.
This is required for the study of the high order statistical
properties of the CMB anisotropy  
at high resolution, crucial to test some cosmological
scenarios predicting localized features (topological defects,
some inflationary models, ...).

\begin{figure}[t]
\vspace{-0.5cm}
\begin{center}
\epsfig{file=cosmo.ps,width=8.cm}
\end{center}
%\vspace{-6.5cm}
\caption{{\sc Planck}
sensitivity (filled square)
in constraining the Thomson optical depth
and the density contrast $\sigma_8$ compared with 
the sensitivity of WMAP 1-yr data (triangle), possibly combined with
the Ly-$\alpha$ forest information (filled circle),
and of WMAP 4-yr data (square). From \cite{PBM_NA}.}
%\vspace{-0.2cm}
\label{cosmo}
\end{figure}

The detection of the polarization B-mode angular power spectrum is within the 
{\sc Planck} capabilities at least over some suitable ranges of multipoles,
but its accurate and exhaustive measure requires a new generation
of dedicated experiments. 
As well known, 
the details of the reionization history strongly affect 
also the amplitude of the polarization B-mode angular power 
spectrum, which depends on the amplitude of tensorial
(gravitational waves) modes and, at small scales, on the lensing
effect.

The cosmic variance uncertainty
and the Galactic foreground contamination,
quite relevant at low multipoles, decreases at middle and 
high multipoles. The atmospheric emission is expected to be less crucial
for CMB polarization measurements than for anisotropy and spectrum ones.
Therefore, 
%the pros and cons of space 
%missions~\footnote{http://universe.nasa.gov/program/inflation.html}
%and 
ground-based observations (\cite{hobson_tac}; see, e.g., the 
VSA project~\footnote{http://www.mrao.cam.ac.uk/telescopes/vsa/index.html})
appear of particular interest for obtaining precise information
at intermediate and high multipoles,
thanks to the high sensitivity that could be 
reached with
very long integration times and/or the use of a 
very large number of receivers.
On the other hand, the space is the favourite site for the accurate 
measure of the CMB polarization at low and intermediate multipoles
(see, e.g., the NASA Inflation 
Probe~\footnote{http://universe.nasa.gov/program/inflation.html}
of the Beyond Einstein program). 

Fig.~4 reports the uncertainty (including cosmic variance and 
instrument sensitivity and resolution)
in the recovery of the CMB polarization
power spectra as achievable with a $\sim$~yr full sky space 
mission discussed in the context of 
the call of mission themes of the ESA Cosmic Vision 2015-2025,
by using the state 
of the art radiometers (right panel) and bolometers (left panel)
at the focus of a set of four $\sim 60$~cm telescopes.

The comparison with Fig.~5 shows that, as long as foreground
polarization anisotropies (and, in particular, the Galactic
contamination) are accurately known and subtracted, 
the sensitivity levels presented above will allow
to accurately measure also the B-mode or, depending
on its intrinsic level, to set significant constraints on it.



\begin{figure}[t]
%%\vspace{-1.5cm}
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=7cm,height=7cm]{sensitivity_clpol_reno.ps_pages1}&
\includegraphics[width=7cm,height=7cm]{sensitivity_clpol_reno.ps_pages2}
\end{tabular}
\end{center}
\caption{Residual uncertainty in the knowledge of the polarization
angular power spectrum (in terms of 
$\delta T = (\ell(\ell+1)C_\ell/2\pi)^{0.5}$; thermodynamic
temperatures are considered)
including cosmic variance and detector
sensitivity and resolution as in principle achievable by the 
next generation of CMB space missions.
Right panel: the case of radiometer technology
(typical sensitivity of $\simeq 0.1-0.25 \mu$K on a pixel of $30'$
side).
Left panel: the case of bolometer technology
(typical sensitivity of $\simeq 0.04-0.12 \mu$K on a pixel of $30'$
side).
In each panel, the different lines refer to frequency
channels at 32, 64, 94, 143, 217 GHz; at increasing frequency 
the error at high multipoles decreases because
of the resolution increasing 
(from instance 1.09$^\circ$ to 0.16$^\circ$ (FWHM))
by using a given telescopes size.  
The cosmic variance has been computed by assuming, for simplicity, 
a constant polarization anisotropy level of 1, 0.1, and 0.01 $\mu$K
in terms of $\delta T$ (lines from the top to the
bottom at low multipoles). Full sky coverage is assumed.}
\label{pol_sensi}
\end{figure}

The possibility to significantly improve our knowledge 
of the CMB spectrum with respect to the current observational
status, in which the COBE/FIRAS data play the major role
in constraining the CMB spectral distortions,
has been recently addressed.
In particular, 
two space mission proposals, 
the DIMES experiment \cite{KOG96},
designed to reach an accuracy close to that of FIRAS
but at centimeter wavelengths, and 
the FIRAS~II experiment \cite{FM02}
which will allow a sensitivity improvement by a factor $\sim
100$ with respect to FIRAS,
open the new perspective to 
detect CMB spectral distortion and not only to set constraints
on them.


DIMES 
%~\footnote{http://map.gsfc.nasa.gov/DIMES/index.html} 
%(DIffuse Microwave Emission Survey) 
\cite{KOG96} is a space mission submitted to the NASA in
1995, designed to measure very accurately the CMB spectrum at wavelengths
in the range $\simeq 0.33 - 15$~cm \cite{KOG96}.
DIMES will compare the spectrum of each $\simeq 10$ degree pixel on the 
sky to a precisely known blackbody to precision of $\sim 0.1$~mK,
close to that of FIRAS.
The set of receivers is given
from cryogenic radiometers
with instrument emission cooled to 2.7~K
operating at six frequency bands
about 2, 4, 6, 10, 30 and 90~GHz using a single external blackbody
calibration target common to all channels to minimize the calibration
uncertainty.
%In each channel, a cryogenic radiometer
%switched for gain stability between an internal reference load and an
%antenna with 10 degree beam width, will measure the signal change as the
%antenna alternately views the sky and an external blackbody calibration
%target. The target temperature will be adjusted to match the sky signal
%in the lowest frequency band, allowing the absolute temperature to be
%read off from the target thermometry with minimal corrections for
%the instrumental signature. With its temperature held constant, the
%target will rapidly move over the higher-frequencies antenna apertures,
%effectively comparing the spectrum of diffuse emission from the sky
%to a precise blackbody. By comparing each channel to the same target,
%uncertainties in the target emission cancel so that deviations from a
%blackbody spectral shape may be determined much more precisely than the
%absolute temperature.
The DIMES design is driven by the
need to reduce or eliminate systematic errors from instrumental artifacts.
%The instrument emission will be cooled to 2.7~K, whereas the calibration
%uncertainty will be minimized by using a single calibration target,
%common
%to all channels. The atmospheric emission will be observed from low Earth
%orbit and the multiple channels measurements will minimize the
%foreground emission problems.
The DIMES sensitivity represents an
improvement by a factor better than 300 with respect to
previous measurements at centimeter wavelengths allowing a significant
improvement of our knowledge on early dissipation processes and
free-free distortions \cite{BS03a}.



%\begin{figure}
%\vspace{-2.cm}
\begin{figure}[t]
%\begin{figure}
\vspace{-0.5cm}
%\begin{center}
%\epsfig{file=fore_sumpol_update_bw.ps,width=15.cm,height=14cm}
\epsfig{file=fore_sumpol_update_bw.ps,width=15cm,height=10cm}
%\end{center}
%\vspace{8cm}
\caption{CMB polarization angular power spectra (E-mode: black
solid line; B-mode: black dashes; B-mode from lensing:
black long dashes) compared with reasonable predictions
for the overall (Galactic plus extragalatic) foreground
polarized angular power spectrum at 30 (green line),
100 (blue line) and 217~GHz (red line). The few recent upper 
limits and measures are reported for comparison 
\cite{polar, pique, compass, kovac2002}.}
%\vspace{8cm}
\label{clpolfore}
\end{figure}
\vspace{8cm}

Fixsen and Mather \cite{FM02} described the fundamental guidelines
to significantly improve CMB spectrum measures at $\lambda \lsim 1$~cm.
A great reduction of the residual noise of cosmic rays, dominating
the noise of the FIRAS instrument, can be obtained by eliminating
the data on-board co-add process or applying deglitching before co-adding,
by reducing the size of the detectors and by using
``spiderweb'' bolometers or antenna-coupled micro-bolometers.
They are expected to show a very low noise when cooled below 1~K
while RuO  sensors can reduce to 0.1~mK the read noise of thermometers.
The Lagrangian point L2 of the Earth-Sun system is, of course, the
favorite ``site'' for FIRAS~II. Also, the calibration can be
improved by order of magnitudes
with respect to that of FIRAS by reducing the contribution to
the calibrator  reflectance  of light from the diffraction
at the junction between the calibrator and the horn.
A complete symmetrical construction of the instrument is
recommended. This allows the cross-check between calibrators
and between calibrators and the sky and to realize
``an end-to-end calibration and performance test before launch''.
According to the authors, FIRAS~II can be designed to have
a frequency coverage from 60 to 3600~GHz
(i.e. from 5~mm to 83~$\mu$m) with a spectral
resolution $\nu / \Delta \nu < 200$ and sensitivity
in each channel about 100 times better than that of FIRAS.

The combination of these two spectrum experiments 
open, at least in principle, the perspectives to detect and 
possibly measure spectral distortions imprinted by energy 
dissipations about 100 times smaller than those corresponding
to the current upper limits set by FIRAS \cite{BS03b}.
%Of course, not only a very good sensitivity, but also an extreme
%control of the all systematical effects and, in particular,
%of the frequency calibration is crucial to reach these goals.

\section{Reionization phenomenological models}
\label{subsec:reion_phen_mod_pol}

The reionization process 
can be described phenomenologically in terms of injection of
additional ionizing photons 
%via the approach by 
%Peebles, Seager and Hu  -  Doroshkevich and Naselsky - Doroshkevich etal 
\cite{psh, dn, dnnn}.
The ionization
fraction of matter, $x_e=n_e/\overline{n}$, can be obtained
from the balance between the processes of recombination and ionization:
\begin{equation}
\frac{dx_e}{dt}=-\alpha_{\rm rec}(T) \nb x^2_e +
\varepsilon_{i}(z) (1-x_e) {{H}}(z),
\label{eq3}
\end{equation}
where 
$\nb(z)$ is and the mean baryonic density at the redshift $z$,
$T$ is the temperature of the plasma, 
$\alpha_{\rm rec}(T)\simeq 4\times 10^{-13} \left(T/10^4
K \right)^{-0.6} {\rm s}^{-1}{\rm cm}^{-3}$ is the recombination coefficient, 
and $\varepsilon_{i}(z)$ is the efficiency of the  
ionizing photon production giving 
the ionizing photon production rate 
%\begin{equation}
${dn_i}/{dt}=\varepsilon_{i}(z) \nb(z) {{H}}(z) \, ;$
$H(z)=1/t_{exp}$, where $t_{exp}=a/(da/dt)$
is the cosmic expansion time, $a$ being here the cosmic scale
factor.


\noindent
The choice of the function $\varepsilon_{i}(z)$
allows to model the ionization history
also in the presence of extra sources of ionizing photons
(e.g. Ly-$\alpha$ and ionization photons from 
primavel stars, galaxies, and active galaxies, or from 
primordial black hole decays, electromagnetic cascades from particle 
release from topological defects or decay of super heavy dark matter, 
...).  

Assuming equilibrium 
between the recombination and the ionization process, 
for any given history of the plasma temperature 
the evolution of the ionization fraction
is given by the solution of the simple second order equation
obtained by the equality ${dx_e}/{dt}=0$. 

\subsection{Late processes}

For late processes, a simple expression  
describing a first reionization at relevant redshifts
followed by a second reionization, 
possibly mimicking the model by Cen \cite{cen2003}, 
has been proposed~\cite{nc03} in the form:

\begin{equation}
\varepsilon_{i}(z)= \varepsilon_{0} \exp
\left[-\frac{(z-\zreio^{(1)})^2}{(\Delta z_1)^2}\right]
+\varepsilon_{1}(1+z)^{-m}\Theta(\zreio^{(1)}-z) \, ;
\label{eq5.0}
\end{equation}
here $\varepsilon_{0}$,
$\zreio^{(1)}$, and 
$\Delta z_1\ll \zreio^{(1)}$ are free
parameters describing the history
of the first epoch of reionization
which significantly decreases at $z > \zreio^{(1)}$;
$\varepsilon_{1}$, $m$, and (again)
$\zreio^{(1)}$ are free
parameters describing the history
of the second epoch of reionization
resulting into a increasing of 
$\varepsilon_{i}(z)$ with the time,
being $\Theta(x)$  the step function.

Although quite weakly in this modelization, because of the dependence
on the temperature as a power of $\simeq -0.6$
of the recombination coefficient, 
the thermal history influences the ionization fraction
evolution. By using the
matter temperature evolution
$T(z)\simeq 270 \left(1+z/100 \right)^2 {\rm K}$
and modifying the ionization history 
in the {\sc cmbfast} code, 
the CMB angular power spectrum, in both temperature
and polarization, has been computed \cite{nc03} for some representative choices 
of the above free parameters.
As shown by the authors
for the case of the E-mode polarization power spectrum,
the differences between different late reionization scenarios
associated to very different parameters are of particular interest
at relatively low multipoles. 
Provided that the contribution from the Galactic foregrounds,
particularly relevant at these multipoles, could be accurately
modeled, the difference between a scenario involving a single 
reionization at $z \simeq \zreio^{(2)}$ and 
scenarios involving a twice reionization could be
detected by the {\sc Planck} polarization accuracy.

%\begin{figure}[t]
%%\vspace{-1.5cm}
%\begin{center}
%\begin{tabular}{cc}
%   \includegraphics[width=7cm,height=7cm]{nc3.eps}&
%   \includegraphics[width=7cm,height=7cm]{diffcen.eps}
%\end{tabular}
%\end{center}
%\caption{Left panel: polarization (E-mode) angular power spectrum for
%late reionization models.
%The dash and dash-dot lines correspond to models with a single full
%reionization starting at $z \simeq 6$ (a) and at $z \simeq 13.6$ (b), 
%respectively;
%the solid and dotted lines correspond to the model described by 
%Eq.~(\ref{eq5.0}) assuming
%$\varepsilon_{0} = 1.3 \times 10^3$, $m=7$ and, respectively, 
%$\varepsilon_{1}=10^9$ (c) and $10^8$ (d).
%Right panel: relative differences between the power spectra shown
%in the left panel compared to {\sc Planck} relative sensitivity  
%(the analogous of Eq.~(\ref{fullvariance}), but for the E-mode;
%$f_{sky}=0.65$)
%with no multipole binning (thick dashes) and with a suitable
%multipole binning (thick solid line). 
%Solid line: model (d) minus model (c); dash-dot line: 
%model (b) minus model (c); dash line: model (a) minus model (c)
%(with MNRAS permission, courtesy 
%of P.~Naselsky and L.-Y.~Chiang).}
%\label{nas_ch_late}
%\end{figure}

\begin{figure}[t]
\vspace{-1.5cm}
\begin{center}
\epsfig{file=vedi_late_all.ps,width=16.cm}
\end{center}
\vspace{-7cm}
\caption{Contour plots of the optical depth and 
of the fractional injected energy associated to the Comptonization parameter
as functions of $\beta$ and $m$ 
in the case of late reionization processes.
Left panel: $\tau$
evaluated by integrating up to $z=0$.
Middle and right panels: $\Delta \epsilon / \epsilon_i \simeq 4u$ 
(in units of $10^{-6}$)
computed by integrating up to $z=0$ and up to $z=5$,
respectively.}
\label{late_all}
\end{figure}


The relevance of the detection of spectral distortions 
has been partially renewed 
\cite{KOG03}
by the WMAP satellite discovery of a
reionization phase at relevant redshifts.

The computation of the CMB spectral distortions associated to 
the reionization parametric model presented here
is strictly related to the detailed description 
of the thermal history.

For these kinds of late processes,   
we assume here a matter thermal history similar to that reported 
by Cen \cite{cen2003}: a matter temperature $T$ in approximate thermal equilibrium with the 
radiation field (i.e. equal to $T_0 (1+z)$) at $z \gsim 27$;
a linear dependence of ${\rm log} T$ on $z$ at subsequent times
to reach a temperature $T^{(1)}$ (assumed here $1.5 \times 10^4$~K
for numerical estimates) at $z=\zreio^{(1)}$, kept then constant 
up to $z=\zreio^{(2)}$ when it rapidly increases up to
a temperature $T^{(2)}$ (assumed here $2 \times 10^4$~K
for numerical estimates) kept then constant up to low redshifts.   

We have implemented this thermal history in the 
equilibrium evolution of the 
ionization fraction and then used 
these thermal and ionization histories to 
compute the Comptonization and free-free distortions
as described in \cite{BDD95} 
by generalizing the code to include also the case of a $\Lambda$CDM model.

In Fig.~\ref{late_all} we report our 
contour plot results for
the optical depth $\tau$ and the fractional energy injection
associated to the Comptonization distortion 
as functions of the free parameters   
$\beta=\varepsilon_{1}/10^9$ and $m$,
by separately showing for $\Delta \epsilon / \epsilon_i$ 
the results of the integration up to
$z=0$ and up to $z=5$ (of course, the difference 
between these results gives the fractional energy injected
in the plasma at $z \le 5$). For simplicity, we report here
the results for an interval of $\beta$ and $m$ producing values of $\tau$ 
close to the current WMAP best fit
\cite{kogutetal03}. 
Although a detailed computation requires to take into account
the dependence of the ionization history on the matter temperature 
evolution, these results can be approximately 
rescaled to different values of $T^{(1)}$ and $T^{(2)}$ by considering 
the linear dependence of the Comptonization parameter on $T$. 
%By comparing the results of Fig.~\ref{late_all} 
%with the sensitivities reported in Table~\ref{tab_3spec_joint},
%it is clear that 
These predicted Comptonization
distortions could detected and possibly measured by 
an experiment with a sensitivity like that of FIRAS~II.
Analogously to the case of the polarization anisotropy signatures,
the difference between the Comptonization distortions by 
models involving a twice reionization (or a 
continuous reionization starting at 
$z \simeq \zreio^{(1)}$)
and models with a single reionization at $z \simeq \zreio^{(2)}$
is comparable or above the FIRAS~II sensitivity.
The free-free distortion parameter $y_B$ results to be too small,
well below the DIMES sensitivity, 
and is not reported here~\footnote{On the contrary, note that
several specific physical models predict free-free distortion
levels larger than those found in this simple modelization
and clearly observable by a DIMES-like experiments
(see, e.g., \cite{BS03b} and references therein).}.


\subsection{High redshift processes}

Models involving a substantial reionization at redshifts, 
$z \simeq \zreio$, much higher than $\zreio^{(1)} \sim 15$
can not be excluded by current data.
A Gaussian parametric form 

\begin{equation}
\varepsilon_{i}(z)= \xi
\exp \left[-\frac{(z-\zreio)^2}{(\Delta z)^2}\right] \, ,
\label{eqc9}
\end{equation}

\noindent
quite similar to that assumed to describe 
the first reionization epoch for late processes,
can be exploited in this context \cite{nc03};
again $\xi$, $\zreio$, and 
$\Delta z$ are free
parameters describing the history
of this high redshift reionization scenario.
Assuming $\Delta z \ll \zreio$ implies the choice 
of a peak-like model.
Again, it is necessary to add the evolution of the matter 
temperature which should peak at typical values 
of $T_p \approx (1-2) \times 10^4$~K. 
In \cite{nc03} it is assumed an extremely short heating phase 
($\delta$-like) about $\zreio$. After the end of the heating phase
the matter temperature is determined by the usual equation
for the electron temperature evolution, dominated, at high redshifts,
by the Compton cooling term. Therefore a set of 
two differential equations, one  
for the ionization fraction and the other for the matter temperature,
describe the problem~\footnote{Simple approximate analytical solution 
can be used in the limit $\xi \ll 1$. We find also that 
the the system can be easily solved through a numerical integration. 
A simple backward differential scheme with a very small time 
step compared to the other relevant timescales does not introduce 
relevant errors in this context.}. 
This modified ionization history has been 
included in the {\sc cmbfast} code to  
computed the CMB angular power spectrum, in both temperature
and polarization, for some representative choices 
of the above free parameters.
As shown by the authors
for the E-mode polarization angular power spectrum,
the differences between different early reionization scenarios
associated to different parameters 
and between them and a scenario involving a single late
reionization at $z \simeq \zreio^{(2)}$
are relevant at low and also at middle multipoles, 
$\ell \sim few \times (10-100)$. 
This is of particular interest in the light of the 
{\sc Planck} polarization accuracy in the 
multipole region of the CMB acoustic peaks
where the contribution from the Galactic foregrounds
is expected to significantly decrease with respect to the level 
it has at low multipoles.

%\begin{figure}[t]
%%\vspace{-1.5cm}
%\begin{center}
%\begin{tabular}{cc}
%   \includegraphics[width=7cm,height=7cm]{nc33.eps}&
%   \includegraphics[width=7cm,height=7cm]{nc34.eps}
%\end{tabular}
%\end{center}
%\caption{Left panel: polarization (E-mode) angular power spectrum for
%early peak-like reionization models.
%The dotted line corresponds to the model with a single full
%reionization starting at $z \simeq 6$ (a);
%the dash, the solid, and the dash-dott lines correspond 
%to the model described by 
%Eq.~(\ref{eqc9}) assuming
%$\zreio =500$, $\Delta z =12.5$
%and, respectively, 
%$\xi= 100$ (b), 10 (c), and 1 (d).
%Right panel: relative differences between the power spectra shown
%in the left panel compared to {\sc Planck} cosmic variance limit
%($f_{sky}=0.65$, thick dotted line; $f_{sky}=1$, thick solid line).
%Solid line: model (b) minus model (a); dash line: 
%model (c) minus model (a); dash-dot line: model (d) minus model (a)
%(with MNRAS permission, courtesy 
%of P.~Naselsky and L.-Y.~Chiang).}
%\label{nas_ch_early}
%\end{figure}

%
\begin{figure}
\vspace{-1.5cm}
\begin{center}
\epsfig{file=vedi_early_all.ps,width=14.cm}
\end{center}
\vspace{-7cm}
\caption{Contour plots of the optical depth, $\tau$,
(left panel) 
and of the fractional energy injection 
associated to the Comptonization parameter, 
$\Delta \epsilon / \epsilon_i \simeq 4u$, 
(right panel)
as functions of $\xi$ and $\zreio$
in the case of early peak-like reionization processes (logarithmic scale).}
\label{early_all}
\end{figure}


For the study of the spectral distortions 
associated to early peak-like reionization processes,
we have numerically integrated the differential equations 
for the ionization fraction and the matter temperature
as described above.
Differently from 
the $\delta$-like assumption 
for the matter temperature during the heating phase
about $\zreio$ (that is not particularly critical 
for polarization anisotropy considerations)
we adopt here a Gaussian parametric form 

\begin{equation}
T(z)= T_p \exp \left[-\frac{(z-\zreio)^2}{(\Delta z)^2}\right] \,  
\label{eqc9_T}
\end{equation}

\noindent
for the matter temperature during the heating phase
(within a redshift interval $\simeq \pm 3 \Delta z$
about $\zreio$) and then assume the usual 
temperature evolution equation, dominated by the  
Compton cooling term, at later epochs
($T_p = 1.5 \times 10^4$~K 
and $\Delta z = 0.025 \zreio$
are adopted here for numerical estimates).
It is in fact quite reasonable to assume a similar
time dependence for both the efficiency of the  
ionizing photon production, $\varepsilon_{i}(z)$, 
and the matter temperature during the active phase.
We assume as initial conditions 
at the beginning of the heating/ionization phase
the thermal equilibrium between matter and radiation
and the residual ionization fraction obtained 
at the considered redshift from the standard 
recombination.

Finally, we have implemented the thermal and ionization history
as described above in the code \cite{BDD95} 
for the computation of the Comptonization and free-free distortions.

In Fig.~\ref{early_all} we report our 
results in terms of contour plots
for the optical depth $\tau$ and the fractional energy injection
associated to the Comptonization distortion 
as functions of the free parameters   
$\xi$ and $\zreio$. These results can be 
rescaled to different choices of 
$T_p$ and $\Delta z$ by using the approximate
proportionality relations between  
$\tau$ and $\Delta z$  and between
$u$ and $T_p \Delta z$~\footnote{In reality, 
for the lowest considered values of $\xi$ ($\xi \approx 1$) 
we find an increasing 
of the Comptonization distortion with 
$\Delta z$ larger by a factor $\approx 1.5-3$
than that suggested by the above proportionality and
related to the different initial conditions 
(the process starts at earlier times) 
and to the different coupling between 
the ionization fraction and the matter temperature.
We find that this holds also for the free-free
distortion parameter $y_B$.}.
Fig.~\ref{early_all} shows that a large region 
of the $\xi$ and $\zreio$ parameter space
can be clearly ruled out by current WMAP data
because of the violation of the limits 
on the optical depth. It is also remarkable
that in the permitted region of $\xi$ and $\zreio$ 
(corresponding to $\tau \sim 0.1$) the model 
predicts values of fractional injected energy 
$\Delta \epsilon / \epsilon_i \simeq 4u \sim 10^{-6}$,
again in principle measurable with the FIRAS~II sensitivity.
We find again values of free-free distortion parameter $y_B$ too small
with respect to the DIMES sensitivity~\footnote{By considering
higher matter temperature values (up to $6 \times 10^4$~K),
we find only a weak dependence of $y_B$ on $T_p$ 
because the typical decreasing of $y_B$ with $T_p$ is approximately
compensated by the increasing of the ionization fraction
because of the decreasing of the recombination efficiency.}. 
 
To summarize, since it is plausible 
to assume peak matter temperatures $\gsim (1-2)\times 10^4$~K 
to have an efficient (late or early) reionization,
values of 
$\Delta \epsilon / \epsilon_i \simeq 4u \sim (1-2) \times 10^{-6}$
should be considered as typical (lower limit) predictions 
for the Comptonization distortion associated to reionization 
scenarios compatible with the WMAP results
\cite{buriganaetal04rev}.



\section{Inhomogeneous reionization in the presence of massive neutrinos}

%\begin{figure}
%\vspace{-2.cm}
%\begin{figure}[t]
\begin{figure}
\vspace{-0.5cm}
%\begin{center}
\epsfig{file=clstar.ps,width=15.cm,height=10.cm}
%\end{center}
%\vspace{8cm}
\caption{The CMB anisotropy power spectra for different neutrino masses
considering (bottom panel) or not (top panel) the 
inhomogeneities of the reionization process.}
%\vspace{1cm}
\label{clstar}
\end{figure}



As a specific example, we have investigated the role of a HDM component in 
the form of three massive neutrino flavors in the context of 
reionization scenarios.
Assuming a flat background cosmology
described by the best fit power law $\Lambda$CDM model with WMAP data 
($\Omega_bh^2=0.024$, $\Omega_mh^2=0.14$, $h=0.72$), 
we analyze the role of the neutrino mass for the properties of the gas 
in the intergalactic medium (IGM). We find that the temporal 
evolution of the hydrogen and helium ionization fractions is 
sensitive to the neutrino mass, with relevant implications for the CMB
anisotropy and polarization angular power spectra.


%\begin{figure}
%\vspace{-2.cm}
%\begin{figure}[t]
\begin{figure}
\vspace{-0.5cm}
%\begin{center}
\epsfig{file=cl.ps,width=15.cm,height=10.cm}
%\end{center}
%\vspace{8cm}
\caption{CMB temperature (left panel) and polarization (E-mode, right 
panel) anisotropy power
spectra obtained for the above reionization model (including
inhomogeneities) by considering or not the neutrino contribution
for a specific value (25) of the reionization redshift.
Note the sensitivity of polarization to the neutrino mass.}
\vspace{1cm}
\label{cl}
\end{figure}


The reionization is assumed to be caused by the ionizing photons produced
in star-forming galaxies and quasars. 
This process depends on the evolution of the background density 
field that determines the formation rate of the bounded objects, 
the gas properties in the IGM and their feedback relation.
At the redshift of collapse, the fraction of the mass of the gas in
the virilized halos can be obtained if the probability distribution 
function of the gas overdensity is known.
The temperature-density relation and the virial mass-temperature relation  
determines the connection between the gas density and the matter density 
at the corresponding scales \cite{PBM_NA}.
During and after recombination,
neutrinos with masses in eV range can have significant interactions 
with photons, baryons and cold dark matter particles via gravity only. 
The neutrino phase-space density
is constrained by the Tremaine-Gunn criterion \cite{tg79} 
that puts limits on the neutrino energy-density inside bounded objects. 
Neutrinos cannot cluster via gravitational instability on scales 
below the free-streaming scale.
%that is related to the causal horizon distance
%and the Hubble expansion rate of the Universe.
The free-streaming distance determines the neutrino energy-density 
distribution inside the gravitationally collapsed objects \cite{pbm02}, 
the temperature-density relation of the gas in the IGM and the hydrogen 
and helium ionization fractions.

%
%\begin{figure}
%\vspace{-2.cm}
%\begin{figure}[t]
\begin{figure}
\vspace{-0.5cm}
%\begin{center}
\epsfig{file=znu.ps,width=8.cm}
%\end{center}
%\vspace{8cm}
\caption{The probability density function of the neutrino
masses (69\% CL) as could be estimated by the {\sc Planck}
mission, using the CMB polarization measurements,
for different reionization redshifts
(fiducial model with $m_\nu = 0.23$~eV).}
\vspace{1cm}
\label{znu}
\end{figure}




In Fig.~8 we show the WMAP data compared with the CMB anisotropy 
power spectra obtained for different neutrino masses
with (bottom) and without (top) considering the 
inhomogeneities of the reionization process.
Fig.~9 compares the CMB temperature and polarization (E-mode) 
anisotropy power spectra obtained for the above reionization model 
(including inhomogeneities) by considering or not the neutrino contribution
for a specific value of the reionization redshift.
Clearly, polarization information greatly helps to distinguish
between the two cases.

Finally, in Fig.~10 we show how in this specific reionization model
the neutrino mass could in principle be constrained by {\sc Planck} 
depending on the assumed reionization redshift.
Note the improvement of the sensitivity to neutrino mass
with the decreasing of the reionization redshift,
as intuitive is because of the corresponding increase of the 
neutrino mass role. 



\section{Conclusion}

The WMAP detection of a high redshift reionization 
calls for a better understanding of the physics of the 
reionization process. Different models predicts different imprints
on the CMB in both temperature and polarization anisotropies
while the presence of late spectral distortions 
(Comptonization like, with 
$\Delta \epsilon / \epsilon_i \sim {\rm some} \times 10^{-6}$, and also 
free-free distortions
with amplitudes strongly dependent on the specific considered 
models) seems unavoidable for reasonable thermal histories
in the context of reionization scenarios compatible with 
WMAP results.

Accurate measures of the CMB properties, such as those expected 
by the forthcoming {\sc Planck} satellite and by  
future experiments will offer the opportunity to 
constrain the ionization and thermal history 
of the universe at moderate and high redshifts.

\vspace*{1 cm}

\noindent{\bf Acknowledgements}

\vspace*{0.3 cm}

\noindent
We thank L.~Danese,
L.~La~Porta, and L.~Toffolatti for collaborations and discussions.
We also thank L.-Y. Chiang, B.~Ciardi, A.~Ferrara, and P.~Naselsky
for useful conversations on the reionization history.
The use of the {\sc cmbfast} code is acknowledged.
Some of the results in this paper have been derived applying the 
HEALPix~\footnote{http://www.eso.org/science/healpix/}
({\it Hierarchical Equal Area and IsoLatitude Pixelization
of the Sphere}) by G\`orski et al.~\cite{ref_healpix}) 
to the WMAP 1-yr data products.
Some of the calculations presented here have been
carried out on an alpha digital unix machine 
at the IFP/CNR in Milano by using some NAG integration codes.
The staff of the LFI DPC in Trieste, where
some simulations have been carried out, is acknowledged.

%\bibliographystyle{custom}
%\bibliography{references} % your references bibliography.bib


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quiqui

While excellent ground-based and balloon-borne 
cosmic microwave background (CMB) anisotropy experiments
have been carried out 
(see, e.g., \cite{cmb_obss};
see also \cite{bers_rev}, and references therein, for a review
on CMB anisotropy measures before WMAP), 
and are currently on-going and planned for the future
to accurately study limited sky regions 
with extreme sensitivity and resolution,
space observations offer a unique 
opportunity to jointly study CMB anisotropy, 
both in temperature and in polarization, 
from very large angular scales to some arcminutes  
and to precisely measure the CMB spectrum 
in the absence of ground and atmospheric contaminations.
After the NASA COBE/DMR \cite{smoot92} 
and WMAP~\footnote{http://lambda.gsfc.nasa.gov} 
\cite{bennett2003}
satellite missions,
the data 
expected from the ESA {\sc Planck} 
satellite~\footnote{http://astro.estec.esa.nl/Planck}
\cite{tauber00} 
will represent 
the next major effort in CMB temperature and polarization 
anisotropy space experiments. Only modest efforts 
in CMB spectrum experiments have been pursued in the 
recent past since the COBE/FIRAS \cite{mather90} results,
probably the first real example of the so-called 
``high precision cosmology'', because of the 
difficulties in further improving
the absolute calibration and, at wavelengths longer than those of
FIRAS, in the necessity to use large size equipments. 
The two recent space mission proposals, 
DIMES~\footnote{http://map.gsfc.nasa.gov/DIMES/index.html} 
(DIffuse Microwave Emission Survey; \cite{KOG96}) 
and FIRAS~II \cite{FM02},
open new perspectives in this CMB field.
After an introduction to 
the theoretical framework 
of CMB cosmology (Sect.~\ref{sec:theoretical_background})
and a concise description of {\sc Planck}, DIMES, and FIRAS~II
(Sect.~\ref{sec:obs}) we mainly focus on some dedicated 
topics of particular interest in the perspectives 
of these observational programs.
We review the present status on 
CMB polarization (Sect.~\ref{sec:pol}) and gravitational waves (Sect.~\ref{sec:gravwave}). 
The details of the imprints on CMB temperature 
anisotropies of dark energy are presented in Sect.~\ref{darken}. 
The implications of the low multipole tail of the anisotropy pattern,  
a scientific output specific of CMB space missions, 
are discussed in Sect.~\ref{lowl}. 
The imprints of the non-linear clustering of dark 
matter, including neutrinos, and the possibility of their
detection with {\sc Planck} are discussed in Sect.~\ref{sec:hdm}.
We compare then the current constraints on energy dissipation processes 
at different cosmic epochs set by the available CMB spectrum measures
with those achievable with experiments like 
DIMES and FIRAS~II (Sect.~\ref{sec:spec_dist}).
The signatures of the cosmological reionization (Sect.~\ref{sec:reionization}) are discussed
in the light of the recent WMAP results 
(see Fig.~\ref{wmapfig})
as a representative case to show 
the complementarity of information of future CMB spectrum and 
anisotropy measures.
Finally, in Sect~\ref{sec:disc} we report a summary discussion of these
perspectives.

\begin{figure}[t]
\vspace{-1.cm}
\begin{center}
\epsfig{file=wmap.eps,width=13.cm,height=11.cm}
\end{center}
\vspace{1cm}
\caption{Temperature (TT, top panel) and temperature-polarization 
(TE, bottom panel) angular power spectrum as determined by WMAP 
after the first year of mission.
Note the cosmic variance uncertainty
relevant at low multipoles (see Eq.~\ref{fullvariance}).
We acknowledge the NASA/WMAP Science Team for 
the use of this image (see \cite{bennett2003} for further details).}
\vspace{0.5cm}
\label{wmapfig}
\end{figure}




%\\

\section{THE COSMIC MICROWAVE BACKGROUND: THEORETICAL FRAMEWORK}
\label{sec:theoretical_background}

In the hot big bang cosmological model, the expansion of the universe 
started about 14 billion years ago from a state with high 
density and temperature
%($\rho \simeq 10^{25}$gr/cm$^3$, $T\simeq 10^2$GeV $\sim 10^{15}$~K 
%at $t\simeq 10^{-8}$~s)
and continues now on with a progressive cooling of the universe.
At high temperatures matter and radiation are tightly coupled.
This holds up to a cosmic time 
$t\simeq 3.79\times 10^5$~yr 
when the temperature drops to $T\simeq 3000$~K,  
the ions can capture the electrons, 
and the atoms (hydrogen, helium, and other light elements)
become to be neutral.
This ``recombination'' process reduce the Thomson scattering 
cross section and photons are free to propagate and, since then, 
they have interacted only gravitationally with matter.
These photons are the cosmic microwave background and,
in the standard recombination scheme (i.e. 
in the absence of reionization), the surface 
surrounding us at the recombination epoch
is called last scattering (LS) surface.

\subsection{CMB anisotropies}
\label{anis_th_fram}

The CMB photons we observe probe the physics of decoupling at LS surface 
and the gravitational potentials from the LS surface to the present time.
The magnitude of temperature anisotropies should be related to matter 
dishomogeinities at the LS surface, the 
%primordial 
seeds from which 
galaxies and stars grew up by gravitational instability. We expect a 
pattern of acoustic oscillations in $\delta T/T$ since photon pressure 
resisted the compression of matter by gravitation infall. CMB photons 
suffered also the gravitational redshift from clumping up of the potential 
on LS surface and on their path to the observer. All these effects can be 
seen in the relation for the observed temperature anisotropies (we 
neglect Doppler effects due to the observer and LS surface motion):
\begin{equation}
\left[ \frac{\delta T}{T} \right]_{\rm obs} = \left[ \frac{\delta T}{T}
\right]_{\rm LS} + \left[ \frac{\delta T}{T}
\right]_{\rm ISW} = \left[ \psi + \frac{\delta T}{T} |_{\rm rad}
\right]_{\rm LS} +
\int_{\eta_{\rm LS}}^{\eta_0} (\phi + \psi)' d y \,,
\label{deltatsut01}
\end{equation}
where by ISW we mean the so-called Integrated Sachs-Wolfe effect,
the prime denotes the derivative with respect to the conformal time, 
$\eta$, and the integration is along the line of sight. The 
contribution at the LS surface is called Sachs-Wolfe effect, in honor of 
the scientists who first computed the CMB temperature anisotropies 
\cite{SW}. 
%Some comments are in order: 
As already mentioned, the 
anisotropies depend on gravity, since photons travel in the metric:
\begin{equation}
ds^2=a^2(\eta)[- d\eta^2 ( 1 + 2\psi ) + dx^i~dx^j~ g_{ij}( 1 - 2 
\phi )]
\end{equation}
where 
$a=(1+z)^{-1}$ (we assume $a=1$ today) 
is cosmic the scale factor, $g_{ij}$ is the spatial metric, 
and $\phi \,, \psi$ are the scalar perturbation in the longitudinal gauge 
(in Eq.~(\ref{deltatsut01}) we have omitted the vector and tensor 
contribution for simplicity). 

The dynamics of both background and perturbations are important for the 
temperature anisotropies. The evolution of the cosmic scale factor 
is given by:
\be
H^2 \equiv \left( \frac{d a}{a^2 d \eta} \right)^2 = 
\frac{8 \pi G}{3} \left[ \frac{\rho_{M}}{a^3} + \frac{\rho_{R}}{a^4} +
\rho_\nu (a) + \rho_{\Lambda} + \frac{\rho_{K}}{a^2} \right] \,,
\ee
where $\rho_M$ and $\rho_R$ are respectively the present energy densities of 
non-relativistic (baryons and cold dark matter, henceforth CDM)
%and massive neutrinos, $\Omega_M=\Omega_b+\Omega_{CDM}+\Omega_{\nu}$)
and relativistic matter (photons);
%relativistic matter (including the contribution from photons and 
%relativistic neutrinos), 
$\rho_\Lambda = {3 \Lambda}/{8 \pi G}$ with $\Lambda$ the 
cosmological constant and $\rho_K = {3 K}/{8 \pi G}$ where $K$ is the 
curvature of the spatial section ($K=0, \pm 1$ for flat, closed and open 
sections); $\rho_\nu (a)$ is the energy density of neutrinos which 
redshifts as $a^{-4}$ when these are (effectively) massless and as 
$a^{-3}$ when their mass becomes dominant. 
For any component, it is useful to define the critical 
density, i.e. the ratio 
of the energy densities relative to the total: 
$\Omega_i = 3 \rho_i/(8 \pi G H_0^2)$, where 
$H_0$ is the Hubble constant and $i = b, R, \nu, K, CDM, \Lambda,$ 
...~~.

The dynamics of perturbations is mainly studied through the 
Boltzmann-Einstein coupled system of linear differential equations 
\footnote{Several interesting effects are non-linear, but 
nevertheless important: the Rees-Sciama effect \cite{rs68}, the 
distortions of anisotropies due to weak lensing by the structure already 
collapsed.
The rescattering effects both erase the CMB primary anisotropies
and generates secondary anisotropies through the Doppler effect 
\cite{ka83}.
Secondary anisotropies at very small scales can be
more efficiently generated by higher order contributions
than by the Doppler effect.
They include the Vishniac effect \cite{ov86, v87}
associated to linear perturbations in the baryon density,
spatial inhomogeneities of the ionization fraction \cite{af99,gh98}
and the kinematic and thermal Sunyaev-Zel'dovich effect
from clusters \cite{sz72} 
(see \cite{lapi, dezottiSZ} for a study on the 
contribution om CMB fluctuations from thermal 
Sunyaev-Zel'dovich effect in primeval galaxies 
and quasars). 
The effects due to neutrino clustering will be 
discussed in Sect. 8.}.
The standard four components (photons, neutrinos, baryons, CDM) are 
studied through a Boltzmann description 
(reduced to a perfect fluid description for non-relativistic matter) 
coupled to the metric fluctuations through the Einstein equations. 
We refer to the important paper by Ma and Bertschinger \cite{mb95} or to 
the book by Dodelson \cite{modern} for details. Some more analytic 
description of CMB physics is presented in Sect.~8.

As we have already said, most of the information
in CMB physics can be extracted by linear physics \footnote{This is true
if there are already dishomogeinities which exceeds the Hubble radius in
the early universe, as in passive models of structure formation (see for
instance the inflationary models). If one considers active models of
structure formation (as for scenarios based on topological defects), then
non-linear physics is needed for seeding the primordial 
dishomogeinities.}.
Henceforth there is a dependence of CMB anisotropies not only on
parameters, but also on initial conditions. The initial condition in which
all the components participate in a ``democratic way'' to the metric
fluctuations is called {\em adiabatic}. The condition in which
metric perturbations are initially zero, but develop because of two
compensating dishomogeinities, is called {\em isocurvature}.
Here we give an example of the different values for the Sachs-Wolfe term
for adiabatic and the radiation-CDM isocurvature mode
\footnote{The radiation-CDM isocurvature mode was studied by 
Bond and
Efstathiou \cite{CDM}. The radiation-baryon isocurvature mode was
introduced by Peebles \cite{baryonrad} and the radiation-neutrino 
mode was
studied by Bucher, Moodley and Turok \cite{BMT}.
These three are the only isocurvature modes
{\em growing with time} known.}.
For the adiabatic mode the velocity potentials scale as
$\Theta = 2 k^2 \psi /a H (3+3 w)$ where $w$ defines the equation of 
state ($w \equiv p/\rho$) and $k$ is the wavenumber; on large scales we 
have that $\delta_\gamma = \delta \rho_\gamma/\rho_\gamma \simeq - 4 a H
\Theta/k^2$, which leads to the familiar result \cite{SW, mb95}:
\be
\left[ \frac{\delta T}{T} \right]_{\rm LS} = 
\left[ \psi + \frac{\delta T}{T} |_{\rm rad} \right]_{\rm LS} =
\left[ \psi + \frac{\delta_\gamma}{4} \right]_{\rm LS} 
\simeq \left[ \frac{\psi}{3} \right]_{\rm LS} \, ,
\label{adia}
\ee
where we have used $w=0$ since we approximate the decoupling time fully in
the matter dominated era. For the radiation-CDM isocurvature mode, the 
metric
fluctuations are zero in the radiation dominated era, but become non-zero
in the matter dominated era. The final result is \cite{SW, modern}:
\be
\left[ \frac{\delta T}{T} \right]_{\rm LS} = 
\left[ \psi + \frac{\delta T}{T} |_{\rm rad} \right]_{\rm LS} 
\simeq \left[ 2 \psi \right]_{\rm LS} \, ,
\label{iso}
\ee
Therefore, on large scales (i.e. low $\ell$), temperature anisotropies
with isocurvature initial conditions are six times larger than 
with adiabatic initial conditions, when metric fluctuations with the same
magnitude are present on the LS surface. This discrepancy on large
scales reflects the overall different shape of the $C_\ell$ with adiabatic
and isocurvature initial conditions, as shown in Fig.~\ref{initial_fig}.

%
\begin{figure}
\vspace{-1.5cm}
\begin{center}
\epsfig{file=initial.ps,width=12.cm,height=7.cm}
\end{center}
%\vspace{-7cm}
\caption{Comparison between the angular power spectrum of temperature anisotropies
for adiabatic initial conditions (solid line) and isocurvature
radiation-CDM (dotted line) and radiation-baryon (dashed line). Note that
the two isocurvature modes are superimposed (dimensionless power spectra
are shown).}
\label{initial_fig}
\end{figure}

The statistics of temperature anisotropy is analyzed in spherical 
harmonics $Y_{\ell \, m}$:

\begin{equation}
\frac{\delta T}{T}(\hat{\gamma})=\sum_{\ell = 1}^{\infty}
\sum_{m= -\ell}^{\ell} a_{\ell \, m}
Y_{\ell \, m}(\hat{\gamma}) \, ,
\end{equation}
where $\hat \gamma$ is the direction in which the observer looks to. 
The correlation function of the temperature anisotropies is:
\begin{equation}
C(\theta) \equiv \langle\frac{\delta T}{T}(\hat{\gamma_1})
\frac{\delta T}{T}(\hat{\gamma_2})\rangle = 
\frac{1}{4\pi}\sum_{l}(2l+1) \, C_\ell \, P_\ell (\cos \theta) \, ,
\end{equation}
where $\cos \theta = \hat{\gamma_1} \cdot \hat{\gamma_2}$ 
and $P_\ell$ is the Legendre 
polynomial. By assuming isotropy around the observer, $a_{\ell m}$ should 
have zero mean, $\langle a_{\ell m} \rangle = 0$, and $C_{\ell}$ 
as variance: 
\begin{equation}
C_\ell \equiv\langle\mid a_{\ell m}^2\mid\rangle
= \frac{1}{2 \ell + 1}\sum_m a_{\ell m}^2 \, .
\end{equation}
The $C_\ell$ spectrum is therefore the lowest non-vanishing statistical 
moment of the distribution of temperature anisotropies. 
The search for non-trivial 
higher moments of the distribution - {\em non-Gaussianities} - is under 
way.

The oscillatory structure of the angular power spectrum is due to the
evolution of temperature anisotropies: prior to recombination photons and
the proton-electron plasma behaved as a single ``baryon-photon fluid''. In
presence of gravity, forced acoustic oscillations in the fluid arise,
described by a driven harmonic oscillator equation. The driving force is
given by gravity, the inertia by the baryons and photons provide the
pressure. Since recombination is nearly instantaneous, CMB anisotropies
provide a snapshot of these acoustic oscillations, with different
wavelength modes being caught in different phases of oscillation.
The first peak in the $C_\ell$ corresponds to a perturbation that became
maximally over-dense when the universe recombined (at 1/4 of an
oscillation). Analogously, the third, fifth, etc.. peaks represent scales
which became maximally over-dense after an extra half period of
oscillation. The even peaks are under-dense modes, which also give rise to
power peaks. The troughs are velocity maxima, out of phase with the
density maxima.
A quasi-exponential damping \cite{silk68} occurs at large $\ell$
(larger than $\approx 1000$), where anisotropies are erased by diffusion.


The spectrum of CMB anisotropies depends on the cosmological parameters.
As already explained, CMB anisotropies depend on the metric fluctuations, 
i.e. on their amplitude, initial conditions and spectrum. 
CMB anisotropies feel also the geometry of the space-time, and therefore 
are sensitive to $K$ and $\Lambda$. The regime of oscillations describe the 
physics of decoupling, and the relative abundances of baryons, CDM and 
relativistic degrees of freedom leave an imprint in the series of peaks and 
valleys. Unfortunately, there is a degeneracy in the $C_\ell$ spectrum: 
different combinations of cosmological parameters predict the same 
spectrum \cite{bondetal_deg}.
In order to break this degeneracy it is useful to 
have information on complementary data, such as anisotropies in 
polarization, but also LSS, Supernovae data, etc ...~~.

%Among the many sectors where PLANCK we wish to mention the chance 
%of measuring a primordial spectrum which does not depend as a simple 
%power 
%law on $k$ without invoking complementary data.

\subsection{CMB spectrum}
\label{spec_th_fram}

The CMB spectrum emerges from the thermalization redshift, 
$z_{therm} \sim 10^6 - 10^7$, 
with a shape very close to a Planckian one, 
owing to the tight coupling between radiation and matter through
Compton scattering and photon production/absorption processes, 
radiative Compton and bremsstrahlung. These processes
were extremely efficient at early times 
and able to re-establish a blackbody (BB) spectrum 
from a perturbed one
on timescales much shorter than the expansion time (see, e.g., \cite{DD77}).
The value of $z_{therm}$ \cite{BDD91a}
depends on the baryon density parameter, 
$\Omega_b$, and the Hubble constant, $H_0$, through the product 
$\Ohat_b =\Omega_b (H_{0}/50)^2$ ($H_0$ expressed in Km/s/Mpc). 

On the other hand, physical processes occurring at redshifts $z < z_{therm}$ 
may lead imprints on the CMB spectrum.
Therefore, the CMB spectrum carries crucial informations on physical
processes occurring during early cosmic epochs
(see, e.g., \cite{DB93} and references therein)
and the comparison between models of CMB spectral distortions
and CMB absolute temperature measures can constrain the
physical parameters of the considered dissipation processes.

The timescale for the achievement of
kinetic equilibrium between radiation and matter
(i.e. the relaxation time for the photon spectrum), $t_C$, is
%
\begin{equation}
t_C=t_{\gamma e} {m c^{2}\over {kT_e}} \simeq 4.5 \times 10^{28} 
\left( T_{0}/2.7\, K \right)^{-1} \phi_e ^{-1} \Ohat_b^{-1}
\left(1+z \right)^{-4} \sec \, ,
\end{equation}
%
where $t_{\gamma e}= 1/(n_e \sigma _T c)$ is the photon--electron collision
time, $\phi_e = (T_e/T_r)$, $T_e$ and $T_r=T_{0}(1+z)$ being 
respectively the electron and the CMB radiation temperature; 
$kT_e/mc^2$ is the mean fractional change of photon energy in a scattering
of cool photons off hot electrons, i.e. $T_e \gg T_r$;
$T_0$ is the present radiation temperature related
to the present radiation energy density by $\epsilon _{r0}={\rm a}T_0^4$
(here ${\rm a}=8 \pi I_3 k^4/(hc)^3$, $I_3=\pi^4/15$);
a primordial helium abundance of 25\% by mass is here assumed.

It is useful to introduce the dimensionless time variable $y_e(z)$ 
defined by
%
\begin{equation}
y_e(z) = \int^{t_0}_{t} {dt \over t_C}
=\int^{1+z}_{1} {d(1+z) \over 1+z} {t_{exp}\over t_C} \, ,
\label{eq_y_e}
\end{equation}
%
where $t_0$ is the present time and
%$z_{rec}$ is the recombination redshift (usually $z_{rec} \simeq 1200$) and
$t_{exp}=1/{H}=1/[(da/dt)/a]$ is the expansion time 
(note the relation, $dt=a\, d\eta$, 
between the cosmic time, $t$, and the conformal time, $\eta$).

As particular cases, 
by neglecting the cosmological constant (or dark energy) 
contribution we have
%
%\begin{equation}
%t_{exp} \simeq 6.17\times 10^{17} \left({H_{\circ} \over 50}\right)^{-1}
%(1+z)^{-1} \left[{\Omega_{nr} (1+z)
%\left({1+\kappa {1+z \over 1+z_{eq}}}\right) -(\Omega _{nr} -1)}\right]^{-1/2}
%\sec \, ,
%\end{equation}
\begin{equation}
t_{exp} \simeq   6.3\times 10^{19} \left({T_0 \over 2.7\, K}\right)^{-2}
(1+z)^{-3/2} \left[\kappa (1+z) + (1+z_{eq})
-\left({\Omega_{M} -1 \over \Omega_{M}}\right)
\left({1+z_{eq} \over 1+z}\right) \right]^{-1/2}
\sec \, ,
\end{equation}
%
$z_{eq} = 1.0\times 10^4 (T_{0}/2.7\, K)^{-4}\Ohat_{M}$
being the redshift of
equal non relativistic matter and photon energy densities
%($\Omega _{nr}$ is the density of non relativistic matter in units of 
%critical density); 
%($\Omega _{m}$ is the density of non relativistic matter in units of 
%critical density); 
$\kappa = 1 + N_\nu (7/8)
(4/11)^{4/3}$, $N_\nu$ being the number of relativistic, 2--component,
neutrino species (for 3 species of massless neutrinos, $\kappa \simeq 1.68$),
takes into account the
contribution of relativistic neutrinos to the dynamics of the
universe\footnote{Strictly speaking the present ratio of neutrino to
photon energy densities, and hence the value of $\kappa$, is itself a
function of the amount of energy dissipated. The effect, however,
is never very important and is negligible
for very small distortions.}, while 
assuming $\Omega_K=0$, $\Omega_{\Lambda}=1-\Omega_M$, 
and neglecting the radiation energy density,
as possible at relatively low redshifts, 
we have
\begin{equation}
t_{exp} \simeq (1/H_0) 
\left[\Omega_M (1+z)^3 + 1-\Omega_M \right]^{-1/2}
\sec \, ,
\end{equation}
where $1/H_0 \simeq 3.1 \times 10^{17} h^{-1}$~sec ($h=H_0/100$). 
  
Burigana et al. \cite{BDD91a, BDD91b} have reported on
numerical solutions of the complete Kompaneets equation \cite{Komp56}
that describes the time evolution
%, $\partial \eta_\gamma / \partial t$,
of the photon occupation number, $\eta_\gamma(\nu,t)$, 
under the combined effect of Compton scattering (resulting into
a second order, linear partial differential equation of parabolic type)
and of photon production processes, namely radiative Compton (RC) \cite{RCref}, 
bremsstrahlung (B) \cite{Bref1, Bref2} plus other possible contributions 
(EM): 

\begin{equation}
{\partial \eta_\gamma \over \partial t}
={1 \over \phi_e} {1 \over t_C} {1 \over x^2}
{\partial \over \partial x} 
\left[{ x^4
\left[{\phi_e {\partial \eta_\gamma \over \partial x} 
+\eta_\gamma(1+\eta_\gamma)}\right] }\right]
+\left[{\partial \eta_\gamma \over \partial t}\right]_{RC}
+\left[{\partial \eta_\gamma \over \partial t}\right]_{B}
+\left[{\partial \eta_\gamma \over \partial t}\right]_{EM} \, .
\end{equation}

\noindent
This equation is coupled to the time differential
equation governing the electron temperature evolution for an arbitrary
radiation spectrum in the presence of Compton scattering, energy losses
due to radiative Compton and bremsstrahlung, adiabatic 
cooling, plus possible external heating sources, $q=a^{-3}(dQ/dt)$,

\begin{equation}
{dT_e \over dt}={T_{eq,C}-T_e \over (27/28)t_{e\gamma}}
-{2T_e \over t_{exp}} +\left[{dT_e \over dt}\right]_{RC,B}
+{(32/27)q \over 3n_ek} \, ;
\end{equation}
here 
$T_{eq,C}=[h\int\eta_\gamma(1+\eta_\gamma)\nu^4d\nu] /
[4k\int\eta_\gamma\nu^3d\nu] \,$ is the Compton equilibrium 
electron temperature \cite{peyraud, ZL70},
$t_{e\gamma}=3mc/4\sigma_T\epsilon_r$, $\epsilon_r \simeq \epsilon_{r0}(1+z)^4$
being the radiation energy density, and 
$x$ is the dimensionless frequency $x = h\nu/kT_{0}$
($\nu$ being the present frequency).

The analysis of the constraints on the thermal
history of the universe set by the current spectrum data
and achievable by future high accuracy measurements 
requires the use of manageable formulae describing spectral distortions
for a wide range of the relevant parameters.

Under the assumptions of $i)$ small distortions,
$ii)$ dissipative processes with negligible
photon production, $iii)$ heating close to be instantaneous
(a good approximation if the timescale for energy dissipation is much
smaller than the expansion timescale) $iv)$ distorted radiation spectrum
initially represented by a superposition of blackbodies
(as is the case for a broad variety of situations of cosmological 
interest) accurate analytical representations \cite{BDD95} of the numerical 
solutions \cite{BDD91a, BDD91b}
for the photon occupation number
$\eta_\gamma$ have been found.
The CMB distorted spectra depend on at least
three main parameters: the fractional amount of energy exchanged between
matter and radiation, $\Delta\epsilon / \epsilon_i$,
$\epsilon _i$ being the radiation energy density before the energy injection,
the redshift $z_h$ at which the heating occurs, and the
baryon density parameter $\Ohat_b$.
The photon occupation number can be then expressed in the symbolic form
%
\begin{equation}
\eta_\gamma = \eta_\gamma (x; \Delta\epsilon / \epsilon_i, y_h, \Ohat_b) 
\, ,
\label{eq_dist_spec_1}
\end{equation}
%
where 
%$x$ is the dimensionless frequency $x = h\nu/kT_{0}$
%($\nu$ being the present frequency), and 
$y_h \equiv y_e(z_h)$ characterizes the epoch when the energy dissipation
occurred, $z_h$ being the corresponding redshift
(we will refer to $y_h \equiv y_e(z_h)$ computed assuming $\phi_e=1$, so 
that the epoch 
considered for the energy dissipation does not depend on the 
amount of released energy).

The form of these analytical approximations is in part suggested by 
the general properties of the Kompaneets equation and by its
well known asymptotic solutions.
For late distortions ($y_h \ll 1$) a superposition of
blackbodies is, to a very good approximation, a solution of the
Kompaneets equation, except at very low frequencies where photon emission
processes are important. When they dominate
the Kompaneets equation reduces to an ordinary differential
equation; in this case, a first order analytical solution  
has been found by Danese and De Zotti \cite{DD80}. 
The Comptonization distortion produced by hot gas at small $z$ is 
a typical example of superposition of blackbodies 
(see \cite{ZS69, ZIS72}).
At the other extreme (early distortions, $y_h \gsim 5$) the solution is well
described by a Bose-Einstein (BE) formula with a frequency dependent
chemical potential. For intermediate values of $y_h$,
$\eta_\gamma$ has a shape somewhere between these two limiting
cases. The shape of the distorted spectra at long 
wavelengths is characterized by a spread minimum of the brightness temperature
for $y_h \lsim 0.5$, and by a minimum at a well defined wavelength for $y_h \gsim 0.5$.
The continuous behavior of the distorted spectral shape with $y_h$ can be
in principle used also to search for constraints on the epoch of the energy exchange.

Of course, by combining the approximations describing the distorted spectrum
at early \cite{SZ70}
and intermediate epochs with the Comptonization distortion
expression \cite{ZS69, ZIS72}
describing late distortions, it is possible to jointly treat
two heating processes (see \cite{BDD95, SB02}
and references therein for a more exhaustive discussion).
                                                                             
Long wavelength measures are particularly sensitive to the
free-free distortion due to its well known dependence
on the frequency. At moderately long wavelengths, where
quite accurate observations can be carried out,
$(T_{th}-T_0\phi_{e,i})/T_0 \simeq y_B/x^2 \, $.
Here $\phi_{e,i}$ is the ratio between the electron and radiation
temperature before the beginning of the dissipation process,
$y_B$ is the so called free-free distortion
parameter \cite{BDD95}, and $T_{th}$ is the (possibly frequency 
dependent) equivalent thermodynamic temperature.
At very long wavelengths the equivalent thermodynamic temperature
approaches the electron temperature because of the
very high bremsstrahlung efficiency.

In the combined analysis of the implications of future CMB spectrum
experiments for energy dissipations at different cosmic times and
free-free distortions it is possible 
to avoid to physically link
Comptonization and free-free distortions
(this is also advantageous because of
their possibly different origins).
Eq.~(15) generalizes then to~\footnote{See left panel of 
Fig.~\ref{constr_dist} for some
examples of typical distorted spectra.}: 
%
\begin{equation}
\eta_\gamma = \eta_\gamma (x; \Delta\epsilon / \epsilon_i (y_h), y_h,
\Delta\epsilon / \epsilon_i (y_h \ll 1), y_B, \Ohat_b) \, . 
\label{eq_dist_spec_2}
\end{equation}

Coupled Comptonization and free-free emission 
are expected in several astrophysical scenarios. For example,
ionized halos in the early stages of galaxy formation \cite{OH99}
can produce a relevant free-free distortions
and coupled Comptonization and free-free distortions
can be produced in the reionization epoch, 
likely occurred at substantial redshifts as
indicated by the WMAP data \cite{kogutetal03}.
The relationship between the free-free distortion and the Comptonization
distortion produced by late dissipation processes 
depends on the details of the thermal history at late epochs
(see, e.g., \cite{DB93, BDD95})
and can not be exhaustively represented by independently 
adopting the two integral parameters $y_B$ and $u$.
In addition, free-free distortions are particularly important at long
wavelengths and may partially mask primeval BE-like distortions.
For cooling processes \cite{stebb_silk}, 
which generate negative distortion parameters,
the effect may be more relevant also at centimeter
wavelengths, but the connection between free-free and Comptonization
distortions becomes even more crucial.

It is also possible to extend the limits
on $\Delta\epsilon/\epsilon_i (z_1)$ for heatings
occurred at $z_h>z_1$, where $z_1$ is the redshift corresponding
to $y_h = 5$, when the Compton
scattering was able to restore the kinetic equilibrium between matter and
radiation on timescales much shorter than the expansion time
and the evolution on the CMB spectrum can be easily studied
by replacing the full Kompaneets equation with the differential
equations for the evolution of the electron temperature
and the chemical potential.
This study can be performed by using the
simple analytical expressions \cite{BDD91b}
instead of numerical solutions.

We remember that the adopted analytical description 
of the distorted spectrum holds also for continuous heating processes,
i.e. by relaxing the above assumption $iii)$,
provided that they occur at quite late
epochs ($y_h \lsim 0.05$) or at early epochs ($y_h \gsim 5$), because of the
properties of the asymptotic solutions.
In the former case, $\Delta\epsilon / \epsilon_i$ is the 
dissipation rate integrated over the relevant time interval;
in the latter case, the proper value of $\Delta\epsilon / \epsilon_i$ 
to be used in Eq.~\ref{eq_dist_spec_1} (or 
of $\Delta\epsilon / \epsilon_i (y_h)$ in 
Eq.~\ref{eq_dist_spec_2})
is given by $\simeq \mu (y_h \simeq 5) /1.4$, where
$\mu (y_h \simeq 5)$ is the chemical potential at $y_h \simeq 5$
produced by the combined effect of the dissipation rate 
integrated over the time (which increases $\mu$) and of 
radiative Compton and bremsstrahlung
%the photon production processes 
(which decrease $\mu$).
In this case, Eq.~\ref{eq_dist_spec_1}
represents a good approximation of the distorted
spectrum  by relaxing also the above assumption $ii)$ provided that
the combined effect of energy injection and photon production
is properly included in the computation of the chemical 
potential $\simeq \mu (y_h \simeq 5)$ (see, e.g., \cite{DB93}). 
For continuous processes at intermediate epochs ($5 \gsim y_h \gsim 0.05$),
the above representation, with a proper ``effective'' value 
of $y_h$, can be used as a first order approximation of the
distorted spectrum.
For dissipation processes widely distributed in time,
from $y_h \gsim 5$ to $y_h \ll 1$ 
[such as the damping of perturbations 
(see, e.g., \cite{daly91_other} and references therein), 
and the radiative vacuum decay (see, e.g., \cite{freese87_other}
and references therein)],
the detailed final spectrum shape will depend on the 
details of the considered process and will show
BE-like and/or Comptonization features more or less relevant 
according to the amount of energy dissipated at early and/or late epochs.

For sake of completeness,
we observe that negative distortion parameters can be produced by
physical processes (e.g., cooling processes \cite{stebb_silk}, 
radiative decays of massive particles \cite{SS83, DB93})
that in general are described by a set of process parameters more complex than 
that considered here (epoch and energy exchange only) and may then produce 
spectral shapes different than those described above. Therefore,
the constraints derived for negative values of 
$\Delta \epsilon/\epsilon_i$ and $y_B$ have to be considered 
only as indicative.

We note that for dissipation processes involving both
energy injections and photon production  
(i.e. by relaxing the above assumption $ii)$) occurring
at $y_h \lsim 5$ the final distorted spectrum will take memory
of the details of the considered physical mechanism.
For example, for some intermediate values of $y_h$ and appropriate 
choices of the relevant parameters, 
the Compton scattering of photons produced by
radiative decays of massive particles may produce 
a final spectrum with a 
practically constant thermodynamic temperature at  
$\lambda \lsim 1$~cm and relevant distortions at 
$\lambda \gsim 1$~cm 
while for a late (i.e. at small $y_h$) 
photon production mechanism producing a quite 
narrow feature in the frequency space   
the Compton scattering is only 
able to just spread in the frequency space 
the injected photons resulting into a quite final localized 
spectral distortion. All these models would clearly 
require dedicated investigations based on the 
numerical integration of the complete Kompaneets equation.  

Among the processes involving both energy and photon injection in the 
plasma, the cyclotron emission associated to a cosmic 
magnetic field, $B$, 
has been recently reconsidered particularly in the context of 
its contribution
to the thermalization 
and evolution of CMB spectral distortions in 
comparison to the role of radiative Compton and bremsstrahlung.
By generalizing an approach able to include 
the contributions from stimulated emission 
and absorption (see, e.g., \cite{AFSH02} 
and references therein) 
a quite simple and general expression for the complete
cyclotron contribution to the Kompaneets equation has been recently
derived \cite{ZIZ03BSZ03}:
\begin{equation}
\left({ \frac{\partial\eta_\gamma}{\partial t} } \right)_{cy} =
K_{cy}\delta(x_e-x_{e,cy})[1-\eta_\gamma(e^{x_e}-1)] \, , 
\end{equation}
where  
\begin{equation}
K_{cy}(z)=\frac{4\pi^2\,e\,c}{3 B(z)}\,n_e=4.64\times10^{-4}\,
\Ohat_b\cdot B^{-1}(z)(1+z)^3 \, {\rm s}^{-1} \, ,
\label{ciclo_eq}
\end{equation}
and the electrons are assumed to be in Maxwellian equilibrium.
The magnetic field, $B$, will be assumed to scale as $B=B_0 (1+z)^2$.
Note that $(\partial \eta_\gamma / \partial t)_{cy}$ is null in the case 
of a blackbody (BB) spectrum while in the presence of a spectral 
distortion its contribution peaks at the 
frequency~\footnote{
In reality, although 
Eq.~\ref{ciclo_eq} represents an approximation good enough for numerical 
estimates, 
the fluctuations in the plasma and in the magnetic field 
remove the $\delta$-like behavior of the cyclotron term
that should be in principle replaced with a proper smooth function.}
$x_{e,cy}= h \nu_{cy} / kT_e = 4.97\times 10^{-5}\cdot \phi_e^{-1} 
(T_0/2.7{\rm K})^{-1} B_0(1+z) \, .$
%\label{ciclo_freq}
%\end{equation}
%where $\phi_e=T_e/T_r$, $T_r=T_0(1+z)$ being the CMB radiation 
%temperature

It is possible to compare the contributions to the photon 
production and energy injection
(respectively 
$\propto \int (\partial \eta_\gamma / \partial t) \nu^2 d\nu$ 
and $\propto \int (\partial \eta_\gamma / \partial t) \nu^3 d\nu$)
from radiative Compton, bremsstrahlung, and cyclotron emission 
in the case of early CMB spectral distortions
obtained by assuming a pure Bose-Einstein (BE) formula 
or a BE-like spectrum with a frequency dependent chemical potential
\cite{SZ70}, as expected under realistic conditions 
for the active phase of a dissipation process generating
an early spectral distortion and for the subsequent stages. 
The differences found by using these two different approximations
for the computation of the cyclotron term are much larger than those 
found for the radiative Compton and bremsstrahlung terms
because of the different frequency locations of their contributions
(in particular 
$x_{e,cy} \ll x_c$, $x_c$ being the 
dimensionless frequency where the absorption timescale for 
radiative Compton and bremsstrahlung equals the timescale, $t_C$, for the 
achievement of the kinetic equilibrium).  
This analysis shows that
the contribution from the cyclotron term 
is comparable to (or possibly larger than) that from radiative Compton and 
bremsstrahlung only for values of $B_0$ larger than
$\approx 10^{-6}$~G 
(\cite{ZIZ03BSZ03}), the exact value depending of 
$\Delta \epsilon / \epsilon_i$ and on the cosmological parameters,
i.e. much larger than 
the typical values observed in the intergalactic medium (see, e.g., \cite{kronberg94})
and of the predictions of the scenarios for the genesis
of cosmic magnetic fields (see, e.g., \cite{genb1genb2genb3} and references
therein).
Similar results are obtained also for late distortions.
Therefore, except for some possible models able to
significantly distort in short time the CMB spectrum 
at dimensionless frequencies $\approx x_{e,cy}$,
the implications of CMB spectrum
data can be then accurately evaluated by neglecting the cyclotron term.

Finally, a completely different kind of late 
distortion~\footnote{It could be also considered, from another point of view, 
as a source of astrophysical foreground (see also Sect.~\ref{sec:foreissue}).}
may be produced by the emission from dust grains at high redshifts, $z \gsim 10$,
(see, e.g., \cite{DraineShapiro1989}), particularly in hierarchical models
which more power at small scales should result into a large dust grain
production at high redshifts \cite{Bond1991}.
Thermal dust grains 
could represent in principle a relevant source of sub-millimeter
emission with a broad spectral shape produced by the 
superposition of gray-body spectra at different temperatures
and emissivity indices, typical of the thermal dust emission,
and widely distributed in redshift (see, e.g., \cite{DezottiToffolatti1989}). 



    \subsection{CMB spectrum -- Perspectives from DIMES and FIRAS~II}
    \label{sec:obs_spec}

The whole set of CMB spectrum observations
can be roughly divided in several frequency ranges 
according to the different experiments 
designed to measure the CMB absolute temperature
and the different sources of 
errors that mainly affect them:

$\bullet$ $0.408 \lsim \nu \lsim 1.0$~GHz -- the uncertainties due to the 
observation
site choice and to the determination of the Galactic contribution dominate;

$\bullet$ $1.4 \lsim \nu \lsim 2.0$~GHz -- the uncertainty on the Galactic 
temperature dominates;

$\bullet$ $2.3 \lsim \nu \lsim 9.4$~GHz -- whilst the Galactic 
contribution decreases,
the uncertainty on the atmospheric temperature contribution becomes important;

$\bullet$ $10 \lsim \nu \lsim 37$~GHz -- where experiments 
have been carried out from ground and also from balloons
(in order to reduce the problem of the atmosphere contamination
by observing at an altitude $\gsim 25$~km);

$\bullet$ above 50~GHz -- at these frequencies the main information 
derives from 
the molecular observations, from balloon-borne and rocket 
(e.g. COBRA \cite{cobra})
experiments, and, in particular from the FIRAS measures on-board the COBE 
satellite~\footnote{In the comparison between the new 
observational perspectives and
the implications of currently available measures (Sect.~\ref{sec:spec_dist})
we do not include 
in the data exploitation the data from the COBRA experiment
nor those based on the analysis of the molecular lines,
falling these experiments in the same frequency range 
of the much more accurate FIRAS measures.}.

The results of a nearly complete set of available measures of the 
CMB absolute temperature are summarized in Fig.~\ref{obsspec}
(see, e.g., \cite{SB00} for a description of the almost complete 
database of the CMB absolute temperatures currently available at 
different wavelengths).

Clearly, the most accurate information on the CMB spectrum has been produced
by the COBE/FIRAS experiment. In
particular, the statistical error associated to the
measure at any channel of FIRAS is very small (0.02$-$0.2~mK,
\cite{fixsen96}) and the scale temperature at which the FIRAS
data are set has a systematic uncertainty of 2~mK 
at 95\% confidence level (CL) mainly related to
the calibration uncertainty \cite{mather99}. 
We remark here that, in spite of this calibration uncertainty,
the current constraints on CMB spectral distortion parameters
%,
%particularly on the fractional energy exchange in the cosmic plasma,
%$\Delta \epsilon / \epsilon_i (z_h)$,
%and then on the dissipation processes in the early universe
mainly rely on the FIRAS spectral shape determination, accurately Planckian within 
the errors; only for the free-free distortion parameter, $y_B$, the available 
data at $\lambda \gsim 1$~cm partially change the FIRAS results \cite{SB02}.


\begin{figure}[t]
\vspace{-0.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7.5cm,height=9cm]{tutti.ps}&
   \includegraphics[width=7.5cm,height=9cm]{firas.ps}
\end{tabular}
\end{center}
\caption{Left panel: summary of CMB spectrum observations 
at all wavelengths (COBE/FIRAS measures reported a simple horizontal
lines). Note the large error bars at long wavelengths.
Right panel: COBE/FIRAS measures as reported 
by \cite{mather94} (calibration at 2.726~K) and
by \cite{fixsen96} (calibration at 2.728~K). Recently 
the temperature scale has been translated to 2.725~K
\cite{mather99} by keeping the same spectral shape and sensitivity
of \cite{fixsen96}
(see, e.g., \cite{SB00} for more details).} 
\label{obsspec}
\end{figure}

The future CMB spectrum experiments considered in this work are
dedicated to improve our knowledge both at the same and at
longer wavelengths with respect to the FIRAS frequency coverage
($1$~cm~$\gsim \lambda \gsim 0.01$~cm).

A recent analysis shows that forthcoming ground and balloon measures
at $\lambda \gsim 1$~cm
with a sensitivity improved only by some factors with respect to those
of available data will allow a better understanding
of free-free distortions but
will have only a very small impact
on the constraints on the possible energy exchanges in the primeval
plasma.
The same holds even for observations
with sensitivities up to $\sim 10$ times better than those
of forthcoming experiments \cite{BS03a}.

For this reason 
we consider here the impact of very high quality
data such those
in principle achievable with space experiments.
We discuss the implications of two representative space mission proposals:
the DIMES experiment \cite{KOG96},
designed to reach an accuracy close to that of FIRAS
but at centimeter wavelengths, and 
the FIRAS~II experiment \cite{FM02}
which will allow a sensitivity improvement by a factor $\sim
100$ with respect to FIRAS.

DIMES 
%~\footnote{http://map.gsfc.nasa.gov/DIMES/index.html} 
%(DIffuse Microwave Emission Survey) 
\cite{KOG96} is a space mission submitted to the NASA in
1995, designed to measure very accurately the CMB spectrum at wavelengths
in the range $\simeq 0.33 - 15$~cm \cite{KOG96}.
DIMES will compare the spectrum of each $\simeq 10$ degree pixel on the 
sky to a precisely known blackbody to precision of $\sim 0.1$~mK,
close to that of FIRAS.
The set of receivers is given
from cryogenic radiometers
with instrument emission cooled to 2.7~K
operating at six frequency bands
about 2, 4, 6, 10, 30 and 90~GHz using a single external blackbody
calibration target common to all channels to minimize the calibration
uncertainty.
%In each channel, a cryogenic radiometer
%switched for gain stability between an internal reference load and an
%antenna with 10 degree beam width, will measure the signal change as the
%antenna alternately views the sky and an external blackbody calibration
%target. The target temperature will be adjusted to match the sky signal
%in the lowest frequency band, allowing the absolute temperature to be
%read off from the target thermometry with minimal corrections for
%the instrumental signature. With its temperature held constant, the
%target will rapidly move over the higher-frequencies antenna apertures,
%effectively comparing the spectrum of diffuse emission from the sky
%to a precise blackbody. By comparing each channel to the same target,
%uncertainties in the target emission cancel so that deviations from a
%blackbody spectral shape may be determined much more precisely than the
%absolute temperature.
The DIMES design is driven by the
need to reduce or eliminate systematic errors from instrumental artifacts.
%The instrument emission will be cooled to 2.7~K, whereas the calibration
%uncertainty will be minimized by using a single calibration target,
%common
%to all channels. The atmospheric emission will be observed from low Earth
%orbit and the multiple channels measurements will minimize the
%foreground emission problems.
The DIMES sensitivity represents an
improvement by a factor better than 300 with respect to
previous measurements at centimeter wavelengths.

Fixsen and Mather \cite{FM02} described the fundamental guidelines
to significantly improve CMB spectrum measures at $\lambda \lsim 1$~cm.
A great reduction of the residual noise of cosmic rays, dominating
the noise of the FIRAS instrument, can be obtained by eliminating
the data on-board co-add process or applying deglitching before co-adding,
by reducing the size of the detectors and by using
``spiderweb'' bolometers or antenna-coupled micro-bolometers.
They are expected to show a very low noise when cooled below 1~K
while RuO  sensors can reduce to 0.1~mK the read noise of thermometers.
The Lagrangian point L2 of the Earth-Sun system is, of course, the
favorite ``site'' for FIRAS~II. Also, the calibration can be
improved by order of magnitudes
with respect to that FIRAS by reducing the contribution to
the calibrator  reflectance  of light from the diffraction
at the junction between the calibrator and the horn.
A complete symmetrical construction of the instrument is
recommended. This allows the cross-check between calibrators
and between calibrators and the sky and to realize
``an end-to-end calibration and performance test before launch''.
According to the authors, FIRAS~II can be designed to have
a frequency coverage from 60 to 3600~GHz
(i.e. from 5~mm to 83~$\mu$m) with a spectral
resolution $\nu / \Delta \nu < 200$ and sensitivity
in each channel about 100 times better than that of FIRAS.

The combination of these two spectrum experiments 
open, at least in principle, the perspectives to detect and 
possibly measure spectral distortions imprinted by energy 
dissipations about 100 times smaller than those corresponding
to the current upper limits set by FIRAS.
%Of course, not only a very good sensitivity, but also an extreme
%control of the all systematical effects and, in particular,
%of the frequency calibration is crucial to reach these goals.


    \subsection{Systematic and foreground issues}
    \label{sec:foreissue}
 
In order to realize further steps in CMB cosmology,
high sensitivity and, for anisotropy measures, high resolution
experiments are of course necessary but not entirely sufficient.
An extremely accurate control of all instrumental systematic effects that 
could in principle affect the measurements (and in practice do it)
is crucial, particularly at the sensitivity levels 
presented above (see, e.g., \cite{menn_rev}, and references therein, 
for a review about recent efforts in CMB anisotropy experiments).   
Except for very high resolution imaging, the thermally stable
and ground/atmosphere free space conditions represent 
the best opportunity for a nearly fully sky survey 
with a duration between $\simeq one$ and $\simeq some$ years.

The range of wavelengths between $\sim 1$~mm and $some$~cm,
containing the peak of the CMB surface brightness, 
is the most favorable for CMB measures being there also
close to the minimum the surface brightness 
from the Galaxy and external galaxies, 
which fluctuations show a minimum at 
about 60~GHz at scales larger than
about half degree \cite{bennett2003}, because of the large scale 
Galactic emission, and at about 100--150~GHz 
because of the contribution from extragalactic
sources at smaller angular scales \cite{toffolattietal98}.

For what concerns the study of the CMB temperature and polarization 
anisotropy and in particular of its angular power spectrum, 
it is also remarkable that the overall angular power spectrum 
of the foregrounds shows a spread minimum at multipoles
between $\sim few \times 10$ and $\sim 10^3$,
just in the region of CMB acoustic peaks,  
again because of the decrease (increase) of the 
Galactic (extragalactic) foreground power spectrum 
with respect to the CMB one 
with the multipole increasing.

In spite of these lucky circumstances, 
the reliability of the cosmological exploitation
of microwave measures at the above sensitivity levels 
has to catch with an extremely accurate knowledge,
modeling, and separation of foreground contributions.

In part motivated by the on-going WMAP mission and by 
the forthcoming {\sc Planck} satellite, dedicated 
accurate blind and non blind 
(see, e.g., \cite{fastica, fasticapol, mem} and references therein) 
methods of component separation on patches and on the whole sky
have been recently developed  
and successfully applied to real and simulated 
microwave anisotropy data, both in temperature
and in polarization~\footnote{
We note that the current results of the polarization degrees of the
extragalactic and Galactic foregrounds are $\lsim some$~\%, i.e. 
comparable to that of the CMB anisotropy,
except for the Galactic synchrotron emission which polarization degree may be
larger by about one order of magnitude 
(see also Sect.~\ref{sec:pol}).}.
They can work on multi-frequency maps (both in real and harmonic space) 
or on time ordered data, the latter choice being 
necessary for the separation of the Solar System components \cite{marisetal03}
or in presence of significant source variability \cite{terenzi02terenzi03}.  
Component separation methods have been designed to include or not 
auxiliary informations from other surveys at different 
frequencies, mainly in the radio and far infrared. While the foreground control 
at the neighbor frequencies clearly help separation methods, 
a large frequency coverage of the considered microwave survey 
is in any case crucial to distinguish CMB from foregrounds
just at the microwave frequency range.
Galactic foregrounds can be also separated by exploiting
their spatial correlation properties (typical 
angular power spectra $C_\ell \propto \ell^{-\alpha}$, with
$\alpha \sim 1.5-3$, very different from those of CMB
fluctuations) and/or the phase correlations of 
the spherical harmonic expansion of the microwave anisotropy
maps \cite{nas_ph} (see also \cite{coles_ph}),
being CMB and foreground phases clearly uncorrelated. 
An efficient removal of the extragalactic sources
can be pursued from one side by exploiting 
radio and far infrared catalogs, from the other side through
dedicated filters (e.g. wavelets \cite{vielva}) able to recognize localized 
features. 
All these methods applied to the {\sc Planck} high quality data
will allow an accurate imaging at least of the most significant 
components of the microwave sky temperature anisotropies.
For the polarization anisotropies, this will be more difficult, albeit
about 100~GHz, where the foreground contamination in polarization
is expected to be minimum, {\sc Planck} will accurately 
measure the E-mode power spectrum and 
has good chances also for the detection of the B-mode power spectrum 
at least at interesting multipole ranges (see Fig.~\ref{cl_pol_nu}).
At low multipoles (see also Fig.~\ref{cl_pol}), 
the sensitivity is not the major limitation, but
the Galactic contamination may be a serious problem (see  
\cite{fasticapol} for a recent analysis).  

Foreground separation in CMB absolute temperature measures is from 
one side simpler than in anisotropy measures since only the 
monopole term is relevant in this context and no detailed
mapping is required. On the other side, the sensitivity
of the proposed experiments calls for a extremely accurate 
knowledge of the foreground monopole. Galactic emission
is clearly anisotropic and its spatial properties could be
exploited for an accurate component separation.
In this perspective, the forthcoming {\sc Planck} data, after an 
appropriate absolute re-calibration, should provide the necessary 
information by allowing both an accurate spatial modeling and 
the identification of sky regions of particular low Galactic 
emission.
On the contrary, extragalactic foregrounds are practically
isotropic when smoothed on scales larger than few degrees 
and, by considering only microwave surveys
at such resolutions, their frequency dependent monopole 
can be separated from the contribution of spectral distortions to the  
CMB monopole only on the basis of their different spectral shapes
(see, e.g., \cite{SB02} for an application to current spectrum data).
The extreme sensitivities of the proposed space spectrum experiments 
clearly open this possibility. 
On the other hand, for the very small spectral distortions 
potentially detectable at these sensitivity levels this analysis may be
difficult, possibly providing ambiguous results. 
A robust separation should necessarily exploit the information
that will be available in the future on the foreground monopole. 
Clearly, the {\sc Planck} and 
Herschel~\footnote{http://astro.estec.esa.nl/SA-general/Projects/Herschel/}
projects will allow a much better modeling of millimeter and
sub-millimeter properties of extragalactic sources 
and of their contribution to the background. 
At wavelengths $\lambda \approx 1~$mm
new dedicated $5-10$~m class telescopes 
[e.g., the South Pole Telescope (SPT) and the Atacama Cosmology Telescope  
(ACT)] are planned to reach the sub-arcmin resolution level 
with an extreme sensitivity, thanks to a very large number of 
receivers located on a wide focal plane.
At $\lambda \gsim 1$~cm, crucial information 
will derive from the on-going~\footnote{http://www.narrabri.atnf.csiro.au/}, 
forthcoming, and future more and more deep ground-based facilities 
dedicated to (mainly radio) extragalactic sources.
The Square Kilometre Array 
(SKA)\footnote{http://www.skatelescope.org/}
with its expected sensitivity level better than $\simeq 100$~nJy
at arcsec resolution up to a frequency of  $\simeq 25$~GHz
will provide a great contribution to the modeling 
of radio-source background and fluctuations at the frequencies 
relevant for the analysis or re-analysis of both
anisotropy and spectrum microwave data.

An exhaustive discussion of foreground impact on 
next and future CMB space missions is out of the scope
of this review and it is clearly a very interesting 
interdisciplinary field between CMB cosmology and Galactic
and extragalactic theoretical and observational astrophysics. 
While referring to dedicated 
works for further information (see, e.g., \cite{Dworld, DBBR04}
and references therein),
we would like to notice that the analysis 
of future significantly improved CMB data will do not catch with the 
current, rapidly improving but still quite uncertain, knowledge 
of foregrounds but will certainly take a large 
advantage from the continuous progress in Galactic and 
extragalactic astrophysics of discrete and diffuse components. 

\section{CMB POLARIZATION}
\label{sec:pol}

The polarization pattern of CMB has been the obscure side of the
anisotropies until few years ago. Although, anisotropies in polarization
should be generated on the LS surface by Thompson scattering, the
polarized signal is predicted to be at the $5-10 \%$ level on small
angular scales and much less on large angular scales \cite{pol}.
The information contained in polarization may help in breaking the
degeneracy of parameters in the temperature anisotropies
\cite{bondetal_deg}.
The polarization signal on large scale may be enhanced by the
reionization occurring at small redshift ($z < 50$). 
The observation of this signature represents the main cosmological goal
of the SPORT project \cite{cortiglioni_sport}. 

The photon polarization is characterized by a $2 \times 2$ intensity
tensor. This tensor is studied through the so-called Stokes parameters,
the intensity $I$, the linear polarization $Q, U$
and the circular polarization $V$
(see, e.g., \cite{balbietal02} and references therein). 
The $V$ signal is not generated by
Thompson scattering (in absence of a magnetic field) and is neglected.
When this polarization modes are taken into account, the
signal $T$ in a direction $\hat \gamma$ is decomposed as \cite{kogutetal03}:
\be
T (\hat \gamma) = I (\hat \gamma) +  Q (\hat \gamma) \cos 2 \alpha + U
(\hat \gamma) \sin 2 \alpha \,,
\ee
where $\alpha$ is an angle which depends on the orientation of
the coordinate system of the observer.
$Q \,, U$ can be analyzed by expanding in spin spherical harmonics
$_2 Y_{\ell \, m}$. Instead of $Q \,, U$, 
whose transformation under the rotation of the
plane orthogonal to the line of sight is not simple, 
it is more useful to define a
linear combination of them. 
The two modes which are obtained
(see Fig.~\ref{cl_pol})
are E and B (which are invariant and pseudo-invariant under parity
transformation).
In this way only four power spectrum are needed to characterize CMB
anisotropies; T, E, B and the cross correlation TE. All the other cross
correlations vanishes for symmetry. This choice of polarization modes is
also useful since the B-mode is only produced by tensor modes at the
linear level, while the E-mode is produced both by scalar and tensor modes.

\begin{figure}[t]
%\begin{figure}
%\vspace{-4.5cm}
\vspace{-0.5cm}
\begin{center}
\epsfig{file=fore_sumpol_afterwmap_rspolnew_noB_bw_lens.ps,width=16.cm,height=7.5cm}
\end{center}
\vspace{0.1cm}
\caption{CMB polarization angular power spectra 
(E-mode, solid line and B-mode, dashes) for a $\Lambda$CDM model
in agreement with WMAP results (cosmological parameters as in the
last column of table~7 of \cite{sper03} 
and a ratio of tensor to scalar quadrupole given by
$7(1-n_s)$ are is assumed) compared to 
$i)$ the lensing contribution \cite{SZlensing} before
(long dashes, two representative cases are reported)
and after (thin long dashes) subtraction assumed accurate
at $\simeq 10$\% level in terms of $C_\ell$,
$ii)$ the measures/upper limits currently available 
for the E-mode \cite{kovac2002, polar, pique, compass},
and $iii)$ current estimates of overall (Galactic emission plus 
extragalactic sources) foreground angular power spectrum     
at 30 (dots), 100 (dot-dashes), and 217~GHz (three dots-dashes).
In particular, for the Galactic dust contribution, dominant at 217~GHz,
we report here the results obtained from the 
94~GHz dust temperature signal template 
(at $|b|\gsim30^\circ$) of the WMAP 1~yr data products 
scaled according to the dust frequency slope \cite{bennett2003}
and the typical polarization degree ($\sim 5$\%) found by 
ARCHEOPS \cite{archeops}
(see also Fig.~\ref{cl_pol_nu} and the text).}
\vspace{0.2cm}
\label{cl_pol}
\end{figure}

The first detection of the E-mode has been claimed by the Degree Angular
Scale Interferometer (DASI). DASI has detected a E-mode
signal at 4.9 $\sigma$ on angular scales $\sim 0.5^�$ and a TE correlation
at 2~$\sigma$ \cite{kovac2002}.
At the time being this review was written the WMAP team has not released
the spectrum for the E mode yet. With the first year release the WMAP team
has released the TE spectrum (see Fig.~\ref{wmapfig}), 
leaving for the second year release the
electric polarization, which seemed affected by some systematics. However,
only with the TE correlation spectrum WMAP was able to probe 
the {\em reionization} and {\em the nature of 
scale fluctuations}. In this section we focus on the latter case.

WMAP detected a large-angle ($50 \lesssim \ell \lesssim 150$)
anti-correlation in the temperature-polarization cross-power
spectrum \cite{kogutetal03, peiris}. This 
anti-correlation is
a distinctive signature of adiabatic fluctuations which exceeds the
horizon on the LS surface. The explanation is that the polarization signal
in the tight coupling approximation comes from peculiar velocities, while
the intensity signal comes from density fluctuations. On large scales the
E-mode goes as a $\sin$, while the T signal as a $\cos$, causing an
anti-correlation. At 2 $\sigma$ the data are still consistent with pure
isocurvature perturbations, while the agreement with topological defects
(as presently studied) seems far.



\section{GRAVITATIONAL WAVES}
\label{sec:gravwave}

The CMB anisotropy pattern is also an indirect probe of gravitational waves
(GW henceforth), the only pure metric fluctuations in Einstein gravity.
A stochastic background of GW at LSS may leave a distinctive imprint
on CMB anisotropies. Since this stochastic background may not 
be directly detectable by
GW dedicated experiments, such LIGO~\footnote{http://www.ligo.caltech.edu}
and LISA~\footnote{http://www.lisa.jpl.nasa.gov}, 
CMB plays a major role in this respect.




The imprint left by GW on CMB anisotropies is different from the one
left by matter dishomogeinities, but is also a much weaker signal
to detect. To be consistent with the treatment given in Sect.~\ref{anis_th_fram}, 
the CMB anisotropies induced by GW are 
\cite{SW,TENSOR}:
\begin{equation}
\frac{\delta T}{T} (\hat \gamma) |_{\rm GW} = - \frac{1}{2}
\int_{\eta_{\rm LS}}^{\eta_0} d y  h_{ij}' \gamma^i \gamma^j
\,,
\label{deltatsut}
\end{equation}
where $h_{ij}$ are the transverse traceless metric perturbations and 
$\gamma^i$ is the component of the direction $\gamma$.
For temperature anisotropies it is also useful to introduce the 
relative amplitude of tensor and scalar fluctuations:
\be
R_{\ell^*} \equiv \frac{C_{\ell^* \, T}}{C_{\ell^* \, S}} \,
\label{ratio}
\ee
evaluated at $\ell=\ell^*$ in our convention. As for other cases, 
a cosmic degeneracy occurs and the
tensor signal has to be disentangled from the scalar one.
The polarization offers the possibility to break this degeneracy, since the tensor signal differs from
the scalar one: while linear matter inhomogeneities produce the 
polarization E-mode, gravitational waves also generate its orthogonal B-mode at the linear level.
However, a contaminating B-mode is also generated by the lensing of the E-mode by
the matter distribution along the line of sight \cite{SZlensing} (an effect which is
second order in fluctuations, but nevertheless important since the E-mode signal is larger
than the B-mode one).

A stochastic cosmological background of GW is produced by the expansion of the
universe \cite{grischuck,starobinsky} and its amplitude and spectrum 
inherits the imprint of the evolution of the Hubble rate in the early 
universe.
Scalar fluctuations do not depend only on the Hubble rate, but also on
physical properties of the effective degree(s) of freedom responsible for
their seeding. Therefore, GW is a very important way to probe the energy
scales of processes occurred in the early universe.

Inflation in general predicts a nearly scale invariant spectrum for GW,
while alternative models 
\footnote{By alternative models we mean those scenarios where the horizon
problem is solved by a slow contraction \cite{GV} (either physical 
\cite{ekpyrotic} or conformally related
\cite{PBB}) rather than accelerated expansion in
Einstein gravity. However, it is important to remember that a dust 
contraction \cite{starobinsky,FB} predicts a scale-invariant spectrum for 
GW, just as inflation. Unfortunately, a successful alternative model which 
contract as dust is not yet known.} predict a blue spectrum, 
which eventually may turn to be interesting for GW interferometers.
A nearly scale invariant spectrum makes the GW contribution
to CMB anisotropies relevant for observations,
making the detection of the B-mode a {\em smoking gun}
for inflation.

Within temperature anisotropies, only with $R_2 > 0.14$ there is the
chance to detect GW by CMB \cite{knoxturner}.
Taking into account polarization and the limitations of lensing,
there is a chance to detect GW if
$R_2 > {\rm few} \times 10^{-5}$ (depending on reionization),
corresponding to a scale of inflation $H > 8 \times 10^{-8} m_{\rm pl}$.
This scale is below the GUT scale, giving a chance to determine
observationally if inflation can be related to GUT theories. However,
inflationary models exist with energy scales as low as the electroweak
scale.

All the above discussions neglect the damping of gravitational waves due to neutrinos,
as recently discussed by S.~Weinberg \cite{weinberg2003}.
According to \cite{weinberg2003}, during the GW reentry into the Hubble
radius, the amplitude of GW may be lowered
by the gravitational interaction with free-streaming neutrinos.

To conclude, without taking into account the observation of
\cite{weinberg2003}, we summarize the present
(theoretical and observational) status on the possibility to detect GW with CMB.
Due to the limitation of lensing,
the B-mode induced by GW may be detected if the Hubble rate during 
inflation is above $H > 8 \times 10^{-8} m_{\rm pl}$ \cite{knoxsong}, 
depending on the inflationary model. In fact, if
inflation occurred with a single field then $R = 16 \epsilon_1$, where
$\epsilon_1$ ($= - \dot H/H^2$) is the first slow-roll parameter which
characterizes the departures of the inflationary phase from a de Sitter
expansion. This means that
inflation may be occurred above the GUT scale, but with a very low
$\epsilon_1$ (like for {\em small-field} models), evading the possibility
to be detected. For single field inflationary model, the present
observations constrain $H < 1.4 \times 10^{-5} m_{\rm pl}$ 
\cite{leachliddle}, leaving a window of more than two order of magnitude 
to explore with future experiments.

\section{DARK ENERGY}
\label{darken}

Evidence for a recent acceleration of the universe has been 
independently found in the SNIa data by two groups \cite{SNIA}. Such 
possibility was also favored by other observational data, 
leading to a cosmic concordance model.

A cosmological constant $\Lambda$ does not exhaust all the possibilities 
in explaining the recent acceleration of the universe, which go under the 
generic name of Dark Energy (DE henceforth) as a component with a 
sufficiently negative equation of state ($w_X \equiv p_X/\rho_X \le 
-1/3$).

DE affects the background evolution and therefore alters the  
positions of the peaks of CMB anisotropies, which are dependent 
on the angular diameter 
distance of the LS surface, which is defined 
as \cite{weinberg}:
\begin{equation}
d_A = \frac{1}{\Omega_K H_0 (1+z_{\rm LS})} \sinh \left[ \Omega_K  
\int^1_\frac{1}{1+z_{\rm LS}} \frac{d x}{\sqrt{\Omega_\Lambda x^4 + 
\Omega_K x^2 + \Omega_M x}}
\right]
\end{equation}
where $z_{LS} \simeq 1100$ denotes the redshift at LS. Increasing 
$\Omega_\Lambda$ $d_A$ decreases, shifting to the lower $\ell$s the 
peaks position of the $C_\ell$ spectrum.

Another distinctive imprint of a late change in the equation of state is 
the time variation of large-scale metric fluctuations, affecting the 
low multipoles of the temperature anisotropy pattern \cite{KS}. 
By considering an initial adiabatic scale-invariant spectrum 
with $\phi_k = A/k^{3/2}$ (taken $=\psi_k$ for simplicity):

\begin{equation}
\langle \left(\frac{\Delta T}{T} \right)^2 \rangle_{\ell}=
\frac{2\ell+1}{\ell(\ell+1)}
\frac{A^2}{36 \pi^2} K^2_{\ell} \ ,
\label{ISWlambda}
\end{equation}
where the coefficient $K^2_l$ is given by
\begin{equation}
K_\ell^2 = 2 \ell(\ell+1) \int_0^{\infty} \frac{dk}{k} \Big[
 j_\ell(k\eta_0)  
%\nonumber\\&&
+ 6 \int_{\eta_r}^{\eta_0} d\eta \, \phi'_k
j_\ell(k(\eta_0-\eta)) \Big]^2 \ ,
\label{Kell}
\end{equation}
$K_\ell = 1$ if CDM is only present, while $K_\ell > 1$ if $\Lambda$ is 
not negligible now (here $j_\ell$ is the Bessel spherical function). 
This effect is due to the time integral 
in Eq.~(\ref{Kell}) being non vanishing when $\Lambda \ne 0$ \cite{KS}. 


A cosmological constant does not exhaust all the possibilities in 
explaining the recent acceleration of the universe. 
If dark energy is not a plain cosmological constant, it can affect CMB in 
two ways. The first is through its background equation of state, which 
differs from $w_\Lambda = -1$. 


The second is directly through its 
inhomogeneities, which add to the standard ingredients of the 
primordial soup, baryon, CDM, photons and neutrinos. 
The most popular choice is to model dark energy 
as a scalar field with a Klein-Gordon Lagrangian \cite{RP}.
This scalar field has been later dubbed quintessence \cite{Q} and should 
be very weakly coupled to visible matter \cite{coupling}. 
However, modeling DE as a scalar field is not the unique possibility and, 
as we will show, restricts the physical characteristic of DE. 

The strategy we will follow is a {\it macroscopic} approach to DE, 
considering the physical properties of DE fluctuations instead of studying 
a single model. Whatever the nature of DE is, it can be modeled 
phenomenologically by a fluid with a time dependent equation of state in 
the background and by the conservation equations (assuming that DE is 
uncoupled to other kind of matter and has only local isotropic pressure):
\begin{eqnarray}
\delta_X ' &=& - (1+w_X) \left( \theta_X - 3 \phi' \right)
+ 3 {\cal H} (w_X \delta_X - \frac{\delta p_X}{\rho_X} ) \nonumber \\
\theta_X ' &=& - {\cal H} ( 1 - 3 c_X^2) \, \theta_X + \frac{c_X^2}{1+w_X}
k^2 \delta_X + k^2 \psi \,,
\label{perturbations}
\end{eqnarray}
where $\delta_X \equiv \delta \rho_X / \rho_X$ is the density contrast, 
$\theta_X$ is the velocity potential, and $\cal H = aH$.
The isotropic pressure perturbation $\delta p_X$ can be written as 
\cite{ECSAM}:
\begin{equation}
\delta p_X = c_X^2 \delta \rho_X + 3 {\cal H}(1+w_X) \frac{\theta_X 
\rho_X}{k^2} \left( c_X^2 - 
\frac{\dot p_X}{\dot \rho_X} \right)
\label{presspert}
\end{equation}
where the last piece vanishes if $p_X$ is just a function of $\rho_X$.
From the above we understand how it is not sufficient to specify 
$w_X (t)$ (and $\Omega_X$ at the present time) to study DE, but one needs 
also to specify its pressure perturbations.

\subsection{Dark energy as a perfect fluid}
\label{perf_fluid}

One of the popular way to parametrize DE is through a perfect fluid with a 
constant equation of state, $p_X = w_X \rho_X$, with $w_X < -1/3$ and 
constant in time -- this parametrization is called sometimes called 
X-matter. This choice is however problematic from the point of view 
of cosmological perturbations: 
by sticking with the assumption of perfect fluid -- $p=p(\rho)$ --, we have 
$c_X^2 = w_X < 0$, leading to negative pressure perturbations and therefore to 
instability on short scales, which is not observed. Such models with a 
negative and constant ratio of pressure over density are therefore 
problematic.

In the framework of perfect fluid models the non-linear equation of state:
\begin{equation}
p_X = - \frac{A}{\rho_X^\alpha}
\label{gcg}
\end{equation}
where $A$ is a constant with dimension $[M^{4 + 4 \alpha}]$ and $0 \le 
\alpha \le 1$, defines a perfect fluid behaving as a cosmological constant 
now ($w_X \simeq -1$) and dust in the past ($w_X \simeq 0$). 
The above model has been dubbed Generalized Chaplygin Gas (GCG).
For $\alpha=1$ a fluid with an equation of state as in Eq.~(\ref{gcg}) is 
a hydrodynamic description of a Born-Infeld Lagrangian (see below) with 
constant potential. For $\alpha = 0$ (taken at the end of calculations) Eqs. 
(\ref{gcg}) and (\ref{perturbations}) describe a $\Lambda$CDM model. 
The models with $0 < \alpha < 1$ interpolate between these two models. 
This class of theories is characterized by $c_X^2 = - \alpha w_X$ (
therefore fluctuations are stable on small scales although the fluid has a 
negative $w_X$) and $\delta p_X = c_X^2 \delta \rho_X$ 
(an extreme case of Eq. (\ref{presspert}) where the pressure depends only 
on density even at first order in perturbations). 

The CMB spectrum predicted by a DE model described in Eq. (\ref{gcg}) has 
been computed in \cite{CF}. The constraint on the DE parameters 
$(w_X \,, \alpha)$ by the WMAP data is shown in Fig. (\ref{gcg_fig}) 
and it is remarkable how CMB alone constrain the model stronger than SN 
\cite{AFBC}. The most 
physically motivated case $\alpha=1$ is ruled out at 3$\sigma$ level 
\cite{AFBC}. 

\begin{figure}[t]
\vspace{-2.5cm}
\begin{center}
\epsfig{file=fig6.eps,width=20.cm,height=9.cm}
\end{center}
\vspace{-0.5cm}
\caption{
WMAP plus SNIa likelihood in the plane \protect\protect\( w_{X} \,,
\alpha \protect \protect \) for GCG model of DE.
The thick gray curves are the confidence
regions for the SNIa (65\%, 95\% and 99\% from dark to light gray); the 
dotted curves the confidence regions for
the CMB; the gray regions represent the combined likelihood (65\%
and 95\% c.l.). As it can be seen, the SNIa constraints add little
information.}
\vspace{1.cm}
\label{gcg_fig}
\end{figure}


The model in Eq. (\ref{gcg}) has also offered to explore the possibility 
in which CDM and DE are unified. The unified model base on Eq. (\ref{gcg}) 
is far from the $\Lambda$CDM best fit by more than 3$\sigma$ with CMB 
alone. For a unified model the comparison with LSS may be even more 
selective (this last point was just partially analyzed in \cite{CF, AFBC}).

%If one insists in working with of $p = p(\rho)$, there is a chance to 
%have possibility of the non-linear equation of state $p = -A/\rho^\alpha$ 
%has been explored in \cite{CF}.


\subsection{Quintessence}
\label{quint}

The most popular model choice is to model dark energy
as a scalar field with a Klein-Gordon Lagrangian \cite{RP}:
\begin{equation}
{\cal L}_{KG} = - \frac{1}{2} g^{\mu \nu} \partial_\mu \phi \partial_\nu 
\phi - V(\phi) \equiv Y - V (\phi)
\label{KG}
\end{equation}
where $V$ is the potential for a scalar field.
This scalar field has been later dubbed quintessence \cite{Q}. 
For quintessence $c_X^2 = 1$ and $w_X$ is given by:
\begin{equation}
w_X = \frac{\dot \phi^2/2 - V}{\dot \phi^2/2 + V} = \frac{Y - V}{Y + V}  
\end{equation}
in Eqs. (\ref{perturbations}). Therefore, in assuming the Lagrangian 
(\ref{KG}), the freedom in the choice of the potential reflects an 
arbitrariness in $w_X$, but $c_X^2$ remains fixed to $1$. As a consequence 
of this latter fact, quintessence fluctuations are gravitationally 
unstable only on scales larger then the Hubble radius, leaving 
very weak imprints on the process of structure formation (see \cite{MPS} 
for a study non-linear effects). For instance, for 
the so-called Ratra-Peebles potential $V(\phi) = 
M^{4+\alpha}/\phi^\alpha$ \cite{RP}, $\alpha \lesssim 2$ at 
2$\sigma$-level is obtained from WMAP data \cite{CD}. 
%(a more stringest constraint can be obtained by fixing $h$ 
%\cite{italy}).

%A multitude of potentials have been suggested in addition to the inverse 
%power-law or exponential ones originally suggested \cite{RP}.
%The interest
%Quintessence could also be non minimally coupled to gravity through the 
%usual $\xi R \phi^2/2$ term, even if $|\xi|$ is constrained to be very 
%small in order to obey to the GR tests.

\subsection{Non standard quintessence}
\label{nonst_quint}

In this case DE is modeled by a generic Lagrangian:
\begin{equation}
{\cal L}_{Q} = p (\phi, Y) \,,
\end{equation}
where $p$ is a generic function of the kinetic term $Y$. Tracking 
solutions exist also for this general class of theories.

The choice ${\cal L}_{Q} = \tilde p (Y)/\phi^2$ has been dubbed {\em 
K-essence} \cite{kess} and its observational consequences have been 
explored in \cite{ECSAM,DCS}. In this case $c_X^2 = p_{,Y}/\rho_{,Y}$ is 
in general different from $1$, although it maybe also larger than $1$, 
leading to fluctuations which travel faster than light.
Another possibility is to use a Born-Infeld Lagrangian \cite{BI}:
\begin{equation}
{\cal L}_{BI} = - V (\phi) 
\sqrt{1 + \frac{\partial_\mu \phi \partial^\mu \phi}{M^4}}
\,,
\label{tach}
\end{equation} 
where $M$ is a mass scale. While the KG field may be seen 
as the field theory extension of a non-relativistic Lagrangian, a BI field 
may be seen as the extension of a relativistic particle.
This class of theories admit tracking solutions \cite{AFtach}, is 
characterized by $c_X^2 = - w_X$ independently
of the form of the potential,  and has $-1 \le w_X \le 0$, i.e. its 
fluctuations travel at most at light speed. 

The CMB anisotropies predicted by the model in Eq. (\ref{tach}) have been 
studied and compared to a standard quintessence case \cite{AFP}. Both the 
theories fit the WMAP data equally well, but their fit is again a little 
bit worst than $\Lambda$CDM \cite{AFP}. 

\subsection{Other Possibilities}
\label{others}

The coupling of Dark Energy to visible matter is severely constrained by 
observations and by particle physics \cite{coupling}, however its coupling 
to CDM is unknown. The possibility of a direct coupling among 
DE and CDM can be probed through observational cosmology, either 
through CMB anisotropies \cite{lucaCMB} or through LSS \cite{lucaLSS}. 

Quintessence may also be non minimally coupled to gravity through the
usual $\xi R \phi^2/2$ term \cite{nonminimal}, even if $|\xi|$ is 
constrained to be very small in order to obey to the GR tests 
\cite{chiba}. 

Another interesting possibility is that the recent acceleration of 
the universe is not due to an additional matter component, but to 
modifications of Einstein gravity on large scales. This possibility has 
been revitalized recently in connections with developments in the contest 
of theories with extra-dimensions, and it is known as Modified Gravity 
\cite{ddg}.

\vspace{1cm}

As a final note, if not as a cosmological constant, DE may also have 
arbitrary initial conditions for its perturbations, which are 
usually assumed adiabatic. In the language of cosmological perturbations, 
isocurvature quintessence perturbations are also possible and therefore 
constraints on the DE parameters may be relaxed by allowing a larger class 
of initial conditions. For tracking quintessence models, however the adiabatic 
condition is justified if the tracking regime starts 
sufficiently early \cite{AFiso}: on large scales (where 
the initial conditions are set) isocurvature quintessence 
perturbations are suppressed during the tracking 
regime \cite{AFiso}. If the tracking regime starts only late compared to 
the end of nucleosynthesis (roughly when initial conditions are set for 
cosmological fluctuations) then an initial isocurvature 
for quintessence (generated during for inflation, for instance) may remain 
and it may leave an observational imprint \cite{AFiso}.
Even if they start in an adiabatic initial condition, 
DE fluctuations may be responsible to increase the ISW in way 
different with respect to the 
$\Lambda$CDM case described in Eq.~(\ref{ISWlambda}).
In more complicate models the additional DE fluctuations on large scales 
may help in discriminating $\Lambda$CDM by a DE model, although cosmic 
variance might make useless the effort.

So far, the multitude of attempts to best fit the present data with a DE
model different of a $\Lambda$CDM model have failed. One of the reason for 
the failure of dynamical DE models is the generic qualitative 
prediction of a ISW larger than 
$\Lambda$CDM, which is unfavored by the data as explained in the next section.

\section{LOW MULTIPOLES}
\label{lowl}

Since low multipoles of the CMB anisotropy pattern can only be 
seen by space missions, we devote a section to this topic.

WMAP is improving \cite{bennett2003} the COBE determination of the dipole 
amplitude,
$3.353\pm0.024$~mK, and direction, 
$(l,b)=(264^\circ.26\pm0^\circ.33, 48^\circ.22\pm0^\circ.13)$.
The WMAP calibration 
(which current accuracy is $\simeq 0.5$\%) 
is based on the modulation of the 
Earth's velocity and not on the dipole itself.
The current WMAP determination of the dipole amplitude is
$3.346\pm0.017$~mK, with a sensitivity improvement with respect to COBE
of $\simeq 30-40$\%.
The sub-degree WMAP resolution clearly implies a 
significantly better improvement in the determination of 
the dipole direction: the accuracy of the WMAP 1~yr result, 
$(l,b)=(263^\circ.85\pm0^\circ.1, 48^\circ.25\pm0^\circ.04)$,
is in fact about 3 times better than that of COBE.
The dipole determination provides a very accurate 
measure of the motion of the observer with respect to the CMB reference 
frame, $(\Delta T/T)_d \simeq V/c$ for a CMB Planckian spectrum,
and then of that of the Local System.

{\sc Planck} will accurately measure the dipole with a 
frequency coverage much wider than that of WMAP.
The dependence of the amplitude of the dipole 
on the slope of the CMB spectrum around each 
observed frequency could be then used, at least in principle, 
as a tool to constrain CMB spectral distortions \cite{dd81lubin82},
in a way independent of absolute 
measures~\footnote{In practice, for distortions below the 
FIRAS upper limits, the interplay between calibration,
removal of possible long-term and spin-synchronous systematics,
and foreground contaminations makes this kind of analysis 
quite delicate. Further investigations are needed.}.

Although we have described in the previous section how the recent 
acceleration of the universe may induce an increase in the low multipoles 
of the CMB patterns by the ISW effect, COBE and WMAP have detected the 
opposite. 

For the quadrupole, after the four year of observations COBE 
detected \cite{hinshaw1996}
\begin{equation}
\Delta T^2_2 = 240 \pm^{340}_{124} \mu K^2 \,.
\end{equation}

After the first year of observation WMAP detected \cite{bennett2003}
\begin{equation}
\Delta T^2_2 = 154 \pm 70\mu K^2
\end{equation}
although in the public data the value reported are a little different 
\cite{E1}. Spergel et al. \cite{sper03} quantify the lack of any 
correlated signal on angular scales greater than $60^\circ$ by computing:
\be
S = \int^{1/2}_{-1} d \cos \theta [ C (\theta) ]^2 
\ee
for $10^5$ models by a Markov Chain. They conclude that the probability 
of finding a value than the observed one is $1.5 \times 10^{-3}$. 
Their conclusions is that  ``this discrepancy could be the signature of 
interesting new physics''.

In the following we shall discuss three issues related to the low quadrupole: 
the issue on the value found by the WMAP team, the statistical significance 
of the low $\ell$ signal and, lastly, the physics which could generate it.
We try to review the present perspective on such issues. 

$\bullet$ Data Analysis 

Tegmark, de Oliveira-Costa and Hamilton \cite{TOH} found different results 
by using their all-sky foreground subtracted map. They found a value for the 
quadrupole which is slightly less low than the value obtained by the WMAP team.
Moreover, they noticed that the strongest contribution to quadrupole and octupole 
comes from the Galactic cut, that the octupole is anomalously planar and 
anomalously 
aligned with the quadrupole (see also \cite{OTZH}). 

Also in this case, the polarized low-$\ell$ multipoles should give a complementary 
information, but not very clarifying in this case. By assuming that the COBE/CMB 
data are not affected by non-CMB effects, 
Dore, Gilder and Loeb \cite{DGL} noticed that at large scale the observed TE signal is discrepant at 
$\sim 99.8 \%$ with the TT signal for the concordance $\Lambda$CDM model 
with reionization $\tau = 0.1$ (this discrepancy decreases at $\sim 98.5 \%$ for 
$\tau = 0.17$).



$\bullet$ Statistical Significance

There have been a great attention of the statistical significance of 
low $\ell$ multipoles, in particular because of the $S$ statistic chosen  
{\em a posteriori} originally used by the WMAP team. Efstathiou \cite{E1} 
reanalyzed this issue and concluded that the occurrence of such low signal 
has a probability of $5-10 \%$, compared to the value 1 in 700 obtained by 
the WMAP team.   


$\bullet$ Physics

A large number of theoretical proposals have been suggested to explain 
a low value in the low multipoles of the CMB anisotropies pattern.

A low signal in the CMB anisotropies pattern may be the imprint of 
negligible fluctuations on very large scales. The presence of a 
break in the primordial spectrum of metric fluctuations has been 
search in a rather desperate way recently \cite{break}. 
There is a weak statistical evidence that this break is around the 
present Hubble radius.

If power on the largest scales seems to be missed in a flat universe, 
another simple possibility is a closed universe, where there is a maximal 
wavelength allowed, as in a box. Indeed WMAP data favored a slightly closed universe 
since the value found for the curvature is to $1 \sigma$ level \cite{sper03}:
\be
\Omega_K = \frac{8 \pi G K}{3 a_0^2 H_0^2} = 0.02 \pm 0.02 \,.
\ee
However, a closed universe is not sufficient to explain such a low signal in the 
low multipoles and a break in primordial spectrum is needed as well \cite{Eclosed}.  
The research on how accommodate a closed universe with inflation is ongoing 
\cite{closed}.

The low signal at low $\ell$ may also a sign of non-trivial topology of space (see 
\cite{levin} for a review). Among the many possibilities, 
so far, a spherical space with dodecahedral topology space seems to account for the WMAP data 
\cite{LWRLU}. It was suggested that such possibility would be tested by finding matching 
circles of angular radius about $35^\circ$ \cite{LWRLU}, but the search for 
circles with radius 
greater than $25^\circ$ in the sky in the WMAP data has given negative result 
\cite{circles}.
This last analysis implies that for wide classes of models, our universe has a topology 
scale larger than $24$ Gpc. Another possibility which would explain the low signal and 
the strange alignment of quadrupole and octupole would be a toroidal universe with one small 
dimension \cite{OTZH}, but again this possibility is ruled out \cite{OTZH}. 

Last, but not least, the low multipoles may be not a CMB signal, but an effect 
due to the super-cluster where we are \cite{raul}. The signal in the low multipoles 
would then be frequency dependent, undetectable for WMAP but feasible for {\sc Planck} 
\cite{raul}.

\section{NON-LINEAR EFFECTS IN CMB ANISOTROPIES IN THE 
PRESENCE OF MASSIVE NEUTRINOS} 
\label{sec:hdm}

As well known, the contribution of hot dark matter to the CMB 
anisotropy power spectrum 
shows up in the multipole range of the secondary acoustic peaks where, 
in particular, the next 
{\sc Planck} data will carry a significant improvement with respect to 
WMAP.
In this section we discuss the CMB secondary anisotropies
induced by the non-linear perturbations in the massive neutrino density
associated to the non-linear gravitational clustering in the non-linear
stages of the evolution of the universe when clusters and super-clusters
of galaxies start to form.
The dynamical role of the massive neutrinos in the gravitational clustering
process was extensively considered in the literature
\cite{tg79, bes80, bs83, m00, pg00}.
The extent to which the massive neutrinos can cluster gravitationally
depends on their mass and the parameters
of the fiducial cosmological model
describing the present universe.
The atmospheric neutrino experiments \cite{fu98, am98}
provides strong evidences of neutrino
oscillations implying  a non-zero neutrino mass,
with a lower limit in the range $\simeq 0.04-0.08$ eV.
The latest measurements of the contribution of the double beta decay
to the neutrino mass matrix \cite{kk01} place
an upper limit on the neutrino mass of $m_{\nu} \leq 0.34$eV per neutrino
(95\% CL).
Due to the effect of the neutrino mass on the growth of the
cosmological structures in the universe, the cosmological observations
are sensitive to the neutrino mass. So far, only upper limits
have been obtained from the cosmological observations.
The WMAP experiment \cite{sper03, ver03}
found $m_{\nu} \leq 0.23$eV per neutrino (95\% CL) from combining
CMB, 2dFGRS and Lyman-$\alpha$ data, assuming three neutrino flavors. \\
Throughout the work we analyze the imprint of the dynamics of the
neutrino gravitational clustering on the CMB anisotropy
power spectrum  for a flat  background cosmology in agreement 
with the best fit power law $\Lambda$CDM model of WMAP 
data \cite{sper03, ver03} with neutrino fractions
$f_{\nu}=\Omega_{\nu}/(\Omega_b+\Omega_{CDM})$=0.06, 0.11, 0.16
corresponding to
$\Omega_{\nu}$=0.022 ($3 m_\nu$=0.78eV), 0.037 ($3m_\nu$=1.35 eV),
0.053 ($3m_\nu$=1.89eV).
This model is also consistent with the LSS data
allowing in the same time a pattern of neutrino masses
consistent with the results from neutrino oscillation
and double beta decay experiments 
($h=0.62$ has been assumed in these numerical computations).

\subsection{The neutrino gravitational infall}
\label{neutr_inf}

In the expanding universe, neutrinos decouple from the other
species when the ratio of their interaction rate to the expansion rate
falls below unity. For neutrinos with masses in the
eV range the decoupling temperature is T$_{D} \sim$ 1MeV, occurring
at a redshift z$_{D} \sim $10$^{10}$ \cite{fkt83}.
At this time neutrinos behave like relativistic particles with
a  pure Fermi-Dirac
phase-space distribution:
\begin{eqnarray}
f_{\nu}(q,a)=\frac{1} {e^{E_{\nu}/T_{\nu}} +1},
\hspace{0.3cm} E_{\nu}=\sqrt {q^2+a^2 m^2_{\nu}} \, ,
\end{eqnarray}
where ${\vec q}$ is the neutrino comoving momentum,
${\vec q}=a {\vec p}$, ${\vec p}$ being
the neutrino 3-vector momentum, $E_{\nu}$ is the energy of
neutrino with mass $m_{\nu}$ and $a$ is the cosmic scale factor.\\
As  neutrinos are collision-less particles, they
can significantly interact with  photons, baryons and cold dark matter
particles only via gravity.
The neutrino phase space density
is constrained by the Tremaine and Gunn
criterion \cite{tg79} 
that put  limits on the neutrino energy density inside
the gravitationally bounded objects:
in the  cosmological models
involving a HDM component (such as CHDM models)
the compression fraction of neutrinos through a cluster,
$f(r)=\rho_{\nu}/\rho_{CDM}$ (where $r$ is the cluster radius),
never exceeds the background
ratio $\Omega_{\nu}/\Omega_{CDM}$.
Because the formation of
galaxies and clusters is a dynamical time process,
the differences introduced in the gravitational
potential due to neutrino gravitational clustering
generate metric perturbations that
affect the evolution  of the density
fluctuations of all the components of the expanding universe.
Fig.~\ref{simul_hdm} presents the  evolution of the
projected mass distributions of cold dark matter plus baryons
and neutrinos obtained from numerical simulations at
some values of the redshift $z$.
One can see that neutrinos accretion, which follows CDM and 
baryons, contributes in the dynamic way to the
gravitational clustering process.\\
\begin{figure}
\vspace{-0.5cm}
\epsfig{figure=f1.eps,width=16cm}
\caption{The evolution with the redshift of the
projected mass distributions of
cold dark matter plus baryons
(upper row) and neutrinos (lower row) obtained from numerical simulation
of $128^3$ cold dark matter plus baryons (the total mass of $8 \times 10^{16} M_{\odot}$)
and $10 \times 128^3$ neutrinos
(the total mass of $4.8 \times 10^{18} M_{\odot}$, $f_{\nu}=0.06$) in a
box of size 128 Mpc (units of axes are in Mpc).}
\label{simul_hdm}
\end{figure}
Neutrinos cannot cluster via gravitational instability
on distances below the free-streaming distance $R_{fs}$
\cite{bes80, bs83, m00}.
The neutrino free-streaming distance is related to the
causal comoving
horizon distance $\eta(a)$ through \cite{dgs96}:
\begin{eqnarray}
R_{fs}(a)=\frac{1}{k_{fs}}=\frac{\eta(a)}{\sqrt{1+(a/a_{nr})^2}}
\,{\rm Mpc},
\hspace{0.35cm}
\eta(a)=\int^a_0 \frac{da}{a^2 H(a)},
\end{eqnarray}
where $a_{nr}$ is the value of the scale factor
when massive neutrinos start to become non-relativistic
($a_{nr}=(1+z_{nr})^{-1} \approx 3k_{B}T_{\nu,0}/ m_{\nu}c^2$).
%and $H(a)$ is the Hubble expansion rate:
%\begin{eqnarray}
%H^2(a)=\frac{8 \pi G}{3}[\Omega_m/a^3+\Omega_r/a^4+
%\Omega_{\Lambda}+\Omega_k/a^3].
%\end{eqnarray}
%In the above equation $G$ is the gravitational constant,
%$\Omega_m=\Omega_b+\Omega_{CDM}+\Omega_{\nu}$
%is the matter energy density parameter, $\Omega_b$, $\Omega_{CDM}$,
%$\Omega_{\nu}$ being the energy density parameters of baryons, cold dark
%matter and neutrinos, $\Omega_{r}$ is the
%radiation energy density parameter
%that includes the contribution from photons and relativistic neutrinos ,
%$\Omega_{\Lambda}$ is the vacuum energy density parameter,
%$\Omega_k=1-\Omega_m-\Omega_{\Lambda}$ is the energy density parameter
%related to the curvature of the universe and $a=(1+z)^{-1}$ is the cosmic
%scale factor. 
$R_{fs}$ defines the minimum linear dimension that a
neutrino perturbation should have in order to survive
the free-streaming.
\begin{figure}
\vspace{-0.5cm}
\setlength{\epsfxsize}{0.80\textwidth}
\centerline{\epsfbox{f2.eps}}
\caption{Panel a): dependence of the
neutrino free-streaming distance $R_{fs}$ on the scale factor.
We show also a specific scale, $\lambda$=20$h^{-1}$Mpc, constant
in comoving coordinates (horizontal dashed line)
and the evolution
with the scale factor of the causal horizon distance
for our cosmological models.
Panel b): dependence on the scale factor of the
mass $M(R_{fs})$ of the perturbation at the scale $R_{fs}$.
We show also the mass of the perturbation at the scale $\lambda$
(horizontal dashed line) and indicate
the typical mass ranges for galaxies (GAL),
groups (GR), clusters (CL) and super-clusters (SCL). }
\label{dep_neutr}
\end{figure}
Fig.~\ref{dep_neutr} presents
the dependence of the causal horizon distance $\eta(a)$,
the neutrino free-streaming distance $R_{fs}$
and of the mass $M(R_{fs})$ of the perturbation at
the scale $R_{fs}$, on the cosmic scale factor \cite{pbm02}.
At early times, when neutrinos  are relativistic,
the free-streaming distance is approximately the causal horizon distance.
After neutrinos become non-relativistic ($a_{nr} \approx 10^{-3}$ for
our cosmological models) the free-streaming distance
decreases with time, becoming smaller
than the causal horizon distance.
The time behaviors of $R_{fs}$ and $M(R_{fs})$
show that neutrino can cluster gravitationally on increasingly
smaller scales at latter times.

In the Newtonian limit, the neutrino gravitational clustering
can be described as a deviation
from the background by a potential $\Phi$
given by the Poisson equation:
\begin{equation}
{\nabla}^2 \Phi({\vec r},a) =4 \pi G a^2
\rho_M(a)\delta_M({\vec r},a) \, ,
\end{equation}
where ${\vec r}$ is the position 3-vector,
$\rho_M(a)$ is the
matter density
and $\delta_M({\vec r},a)$ is the matter density
fluctuation;
$\delta_m=(\rho_b \delta_b + \rho_{CDM} \delta_{CDM}
+ \rho_{\nu} \delta_{\nu})/ \rho_M$, where
$\rho_{CDM}$, $\rho_b$, $\rho_{\nu}$ and
$\delta_{CDM}$, $\delta_b$, $\delta_{\nu}$
are the density and density fluctuations
for cold dark matter particles, baryons and neutrinos. \\
The equations governing the motion of each particle species
(cold dark matter plus baryons and neutrinos)
in the expanding universe
are given by \cite{gb94}:
\begin{eqnarray}
\frac{{d \vec q}}{da}= -a\,H(a) \, {\vec \nabla} \Phi ,
\hspace{0.5cm}  \frac{ d{\vec r} } { da }
={\vec q}\, (a^3 \, H(a))^{-1},
\end{eqnarray}
where ${\vec q}$ is
the comoving momentum and $H(a)$ is the Hubble expansion
rate given by the Eq.~(3).
The Newtonian description
applies in the limit of the weak gravitational field if, at each time step,
the size of the non-linear structures
is much smaller than the causal horizon
size (the background curvature is negligible).   \\
The perturbed neutrino comoving
position  ${\vec r}( {\vec r_0}, a)$ and its peculiar
velocity ${\vec v}( {\vec r_0},a)$ is related to the
fluctuations of the density field
$\delta \rho({\vec r_0},a,k)$ through \cite{zel70}:
\begin{eqnarray}
{\vec r}( {\vec r_0},k,a) &=& {\vec r_0}+D(k,a)
{\vec d}({\vec r_0}) \, , \;\;\;
{\vec v}( {\vec r_0},k,a) = {\dot D}(k,a){\vec d}({\vec r_0}) \, , \\
{\vec \nabla}{\vec d}({\vec r_0})
&=& D^{-1}(k,a) \delta \rho({\vec r_0},k,a) \nonumber \, ,
\end{eqnarray}
where ${\vec r_0}$ is the coordinate corresponding to the
unperturbed comoving position,
${\vec d}({\vec r_0})$ is the displacement field
and $D(k,a)$ is the growth function of the density perturbations.

\subsection{Imprints of neutrino gravitational
clustering at {\sc Planck} angular scales}
\label{neutr_impr}

The neutrino gravitational clustering
 affects both the homogeneous and the inhomogeneous components
of the gravitational field.
The changes in the  homogeneous component
of the gravitational field
are determined by the
changes of the energy density of neutrinos and cold dark matter particles
plus baryons. They affect the Hubble expansion rate,
the sound horizon distance and the neutrino
free-streaming distance.
The changes in the  inhomogeneous component
of the gravitational field are determined by the
changes in the energy density for all matter components
and the changes in the neutrino phase space distribution function.
They affect
the growth of the energy density perturbations of
cold dark matter, baryons, photons, massive and massless
neutrinos.  \\
The characteristic angular scale left by the
the neutrino gravitational clustering on the CMB
anisotropy power spectrum is given by:
\begin{equation}
\theta=\frac{R_{fs}}{\eta_0-\eta(a)},
\end{equation}
where $R_{fs}$ is the scale of the filtering perturbation
with the mass $M(R_{fs})$,
$\eta(a)$ is the particle horizon distance
at the time at which the non-linear perturbation mode
$k$ cross the horizon
and $\eta_0$ is the particle horizon at the present time.
Fig.~\ref{scal_exp} (left panel) presents the evolution of the
characteristic scale $\theta$ and of the corresponding
multipole order of the CMB anisotropy power spectrum  with
the mass $M(R_{fs})$.

\begin{figure}[t]
\vspace{-0.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7cm,height=7cm]{f9.eps}&
   \includegraphics[width=7cm,height=7cm]{f12.eps}
\end{tabular}
\end{center}
\caption{Left panel: evolution of the characteristic angular scale
$\theta$ of the neutrino gravitational clustering
with $M(R_{fs})$ for different neutrino fractions.
We report also the corresponding multipole orders
$l\sim \theta^{-1}$ of the CMB anisotropy power spectrum.
Right panel: confidence regions of the $f_{\nu} - M$ parameter space
as potentially detectable by {\sc Planck} by using the CMB
anisotropy measurements in the presence of the gravitational clustering
assuming known the other main cosmological parameters (grey regions) or
by jointly recover $f_{\nu}$, $M$ and the other main cosmological
parameters (solid lines).}
\label{scal_exp}
\end{figure}
Clearly, new high sensitivity and resolution
space anisotropy experiments will have the
capability to detect the neutrino gravitational clustering 
effect in the CMB angular power spectrum, 
reported for this model in Fig.~\ref{cl_hdm} 
by using different filtering mass values $M(R_{fs})$
and for different neutrino fractions and different values 
of the richness ${\cal A}$ 
of the cluster~\footnote{
According to \cite{kas98},
%Kashlinsky,
the relation between the
mass of the perturbation and the richness ${\cal A}$
of the corresponding cluster can be written in the form
$M=M_{{\rm Coma}} {\cal A}/{\cal A}_{{\rm Coma}}=
1.45 \times 10^{15}\left({\cal A}/106\right) h^{-1}M_{\odot} \, .$}.

\begin{figure}
\vspace{-5cm}
\epsfig{figure=cl_val.eps,width=15cm,height=10cm}
\caption{The  imprint of the neutrino
linear and non-linear gravitational clustering on the CMB
anisotropy power spectrum expressed in terms of $\Delta T/T$
obtained for the filtering perturbation with the mass $M$.
We report in the panels the richness
of these perturbations from the bottom to the top
according to the increasing of the power at multipoles
about $\ell \sim 750$.
In each panel, the dashed line corresponds to  the fiducial
$\Lambda$CHDM cosmological model, without including the non-linear effects
of neutrino gravitational clustering.}
\label{cl_hdm}
\end{figure}

In particular, {\sc Planck} will measure the CMB angular power spectrum
with very high sensitivity up to multipoles $\ell \sim 1000-2000$
with a stringent control of the systematic effects.\\
Fig.~\ref{scal_exp} (right panel) presents few confidence regions
of the $f_{\nu} - M$ parameter space that can be potentially detected by
{\sc Planck} surveyor by using the CMB anisotropy measurements
in the presence of the gravitational clustering, under the hypothesis
that the other cosmological parameter can be measured with other
observations (grey regions) and by using the {\sc Planck} data to
jointly determine $f_{\nu}$, $M$ and the other cosmological parameters 
(solid lines).
We consider for this computation only the {\sc Planck} ``cosmological''
channel between 70 and 217~GHz, a sky coverage $f_{sky}=0.8$
and neglect for simplicity the
foreground contamination \cite{pbm01}. 
By assuming
known the other main cosmological parameters,
we obtain a neutrino
fraction $f_{\nu} \approx 0.011 \pm 0.007$ for an accreting mass
$M \approx (8.2 \pm 3.1) \times 10^{14} h^{-1}M_{\odot}$
(errors at 68\% CL).
The {\sc Planck} surveyor will have
in principle the capability
to measure the non-linear imprints of the neutrino gravitational
clustering on the CMB anisotropy power spectrum for a neutrino
mass range in agreement with that
indicated by the astroparticle and nuclear physics experiments
and a cosmological accreting mass comparable
with the mass of the known clusters.
Of course, even with the high sensitivity and resolution
of {\sc Planck} it is hard to firmly constrain $f_{\nu}$ and $M$
by jointly recovering the other cosmological
parameters, a goal that can be achieved in combination
with other precise cosmological information, such as
galaxy large scale structure surveys, measures of element abundances
from big-bang nucleosynthesis and Type 1a supernovae observations.

\section{IMPLICATIONS OF FUTURE CMB SPECTRUM EXPERIMENTS}
\label{sec:spec_dist}

One of the most intriguing observational aspect 
of CMB spectrum is the well known disagreement between the 
(lower) average of the absolute temperature measures at 
$\lambda \gsim 1$~cm
and the (higher) CMB temperature found by FIRAS. 
It could be likely due to the large
uncertainties, from both instrument systematic effects and 
foreground contamination, of current long wavelength measures.
On the other hand, it is clear that the accurate knowledge 
of the CMB spectrum on a frequency range larger than that 
covered by FIRAS represents
a crucial test for the current cosmological models,
other than a valuable experimental challenge. 
In fact, several classes of physical processes might have left
imprints on the CMB spectrum. For early processes
they are expected to be particularly relevant at long
wavelengths because of their BE-like shape while
processes generated at intermediate epochs 
could present highly model dependent, and widely different, 
spectral shapes. 

By leaving the investigation of the implications of future 
spectrum experiments for the whole set of possible models,
we summarize in this section the new perspectives open for
the quite standard and well-established class of spectral distortions
presented in Sect.~\ref{spec_th_fram}.
The limits on the amount of energy possibly injected in the cosmic
background at arbitrary primordial epochs corresponding to a redshift $z_h$ (or 
equivalently to $y_h$)
have been discussed in several papers
(see, e.g., \cite{BDD91b, NS98}). 
In particular, in the work by Nordberg and Smoot \cite{NS98}
the CMB absolute temperature data are compared with theoretical spectra 
distorted by a first heating process at $y_h=5$, 
a second one at $y_h\ll 1$ and by free-free emission, to derive limits on the
parameters that describe these processes. 
This analysis has been recently generalized \cite{SB02} by considering 
the full range of epochs for the early 
and intermediate energy injection
process by taking advantage of the analytical representation 
of spectral distortions discussed in Sect.~\ref{spec_th_fram}
and by properly combining 
FIRAS data with longer wavelength measures 
by taking into account the FIRAS calibration uncertainty.

In general, 
the above models
of distorted spectra 
can be compared with 
the available measures of the CMB absolute temperature
by using a standard $\chi^2$ analysis. 
The impact of future measures can be addressed
by replacing the available measures with
ideal CMB spectrum data simulated
according to a Planckian shape and/or to the above distorted models 
at the frequencies of the considered experiment
by fouling them to simulate real measurements affected by instrumental
noise~\footnote{Neglecting systematic effects, the last step can be 
realized by adding random numbers
simulated according to a Gaussian distribution with null mean
and rms equal to the instrumental expected sensitivity
to the ideal data.}.

\subsection{Implications of a DIMES-like experiment}
\label{sec:spec_dimes}
 
As a first case, 
we consider the impact of very high quality
data at long wavelengths, such those
in principle achievable with a space experiment like
DIMES \cite{KOG96},
planned to measure the CMB spectrum
at $0.33 \lsim \lambda \lsim 15$~cm with a sensitivity of
$\sim 0.1$~mK,
close to that of FIRAS.

Fig.~\ref{constr_dist} shows typical spectra
associated to a choice of distortion parameter values
potentially measurable by DIMES for different epochs
of the earlier energy injection (left panel)
and the recovery of the fractional energy 
injected at different cosmic times,
corresponding to $y_h$ in the range 0.01--5, 
assuming a single energy injection 
with $\Delta \epsilon / \epsilon_i = 5 \times 10^{-6}$
occurring at known epoch, as well as the implications
for energy dissipations at high redshifts (at $y_h \gsim 5$) 
derived by extending the constraints set at $y_h = 5$
(right panel).
Note the significant improvement achievable for processes
at high redshifts.

In Tables~\ref{tab_3spec_joint} and \ref{tab_1spec} we report the 
contraints on $\Delta \epsilon / \epsilon_i$
achievable with DIMES 
assuming an underlying Planckian spectrum 
respectively by jontly considering
three kinds of spectral distortions 
(an energy injection at intermediate/high $y_h$ ($\gsim 0.5$),
a late energy injection, and a free-free distortion)
and by considering a single kind of spectral distortion
(the epochs of the energy injection are assumed known).

It is evident that such high quality data will
improve by a factor $\sim 50$
the accuracy of FIRAS results on
$\Delta\epsilon/\epsilon_i$ for
dissipation processes
possibly occurred
at intermediate and high redshifts ($y_h \gsim 1$)
and will be crucial for our knowledge of
free-free distortions,
while the constraints on the 
possible late energy dissipations could be improved by about a factor
of two with respect to those set by FIRAS \cite{BS03a}.
By relaxing the assumption to known the epoch of 
the energy injection, it is found \cite{BS03a} 
that such measures could set also
significantly constraints on the epoch of the
energy injection at least for processes 
at intermediate and high redshifts ($y_h \gsim 1$).

\begin{figure}[t]
\vspace{-0.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7.5cm,height=7.5cm]{all_dist.ps}&
   \includegraphics[width=7.5cm,height=7.5cm]{dimes_5e-6_evo.ps}
\end{tabular}
\end{center}
\caption{Left panel: distorted spectra in the presence of 
a late energy injection with $\Delta \epsilon / \epsilon_i = 5 \times 10^{-6}$
plus an early/intermediate
energy injection with $\Delta \epsilon / \epsilon_i = 5 \times 10^{-6}$
occurring at $y_h=5, 1, 0.01$ (from the bottom to the top; 
in the figure the cases at $y_h=5$ and 1 are indistiguishable 
at short wavelengths; solid lines) and plus a 
free-free distortion
with  $y_B=10^{-6}$ (dashes). 
Right panel: constraints on the energy exchanges
derived at different cosmic times by considering
the case of a single dissipation process
on the basis of the
FIRAS data
and data simulated as in the case of an energy injection
with $\Delta\epsilon/\epsilon_i$ equal to (or, at $y_h \gsim 5$, larger than)
$5\times10^{-6}$ and observed with a DIMES-like experiment.
The dissipation epoch is assumed to be known
(is the same in the generation of simulated data and in the fit).
The different lines refer to the best fit result
(dots) and to the upper and lower limits at 95\% CL
(solid lines).
The arrows indicate that the sign of
the lower limit changes at $y_h \simeq 1$, where lower and upper error bars
result to be very similar.
%(from \cite{buriganasalvaterra02}, 
%with MNRAS permission; see also the text).
}
\label{constr_dist}
\end{figure}


\subsection{Implications of a FIRAS~II-like experiment}
\label{sec:spec_firasii}

Similar analyses can then repeated but
by focussing on the cosmological implications of a space experiment
at $\lambda \lsim 1$~cm
like FIRAS~II \cite{FM02}, recently proposed to improve the FIRAS
results of about two orders of magnitude,
and with a particular attention to late dissipation processes. 
Clearly, the sub-millimetric emission from unresolved distant galaxies 
represents a significant source of isotropic 
foreground contamination which long wavelength tail may be also
important at millimetre wavelengths.
Exploiting the whole FIRAS~II frequency range is of course necessary 
to accurately separate the contributions 
of CMB spectral distortions and the extragalactic foreground
to the monopole signal. To first approximation, one could 
ignore at all the information contained in the decade at the 
highest frequencies of FIRAS~II and use only the data at 
$\lambda \gsim 800 \mu$K neglecting the problem 
represented by the millimetric foreground.
The representative results 
obtained in this way by assuming an underlying Planckian spectrum
are reported again in Tables~\ref{tab_3spec_joint} and \ref{tab_1spec}.
Note the significant improvement 
on the constraints on $\Delta\epsilon/\epsilon_i$ 
achievable for processes occurring at any cosmic epochs
while the improvement on the constraints on the free-free distortion
is about one order of magnitude poorer than that achievable
with DIMES \cite{BS03b}.

\subsection{Combining DIMES and FIRAS~II}
\label{sec:spec_dimes_firasii}

The high accuracy on the large frequency coverage 
achievable by combining the data from a DIMES-like experiment
with those from a FIRAS~II-like experiment
could in principle change significantly our vision of the capability of the CMB 
spectrum information to constrain physical processes 
at different cosmic ages \cite{BS03b}
(see also Sects.~\ref{subsec:reion_phen_mod_spec} 
and \ref{subsec:spec_dist_mod}).
We report here some of the results obtained by simulating a quite large
set of possible observational conditions including Planckian and 
distorted spectra as input cases.

The sensitivity in constraining the level of spectral distortion parameters
under the quite general assumption of the possible presence of both
early (BE-like) or intermediate and late (Comptonization
plus free-free) distortions is reported
and compared with the current observational status
in Table~\ref{tab_3spec_joint} and Fig.~\ref{constr_bb} (see again
Table~\ref{tab_1spec} for
the constraints obtained by assuming a single kind
of spectral distortion).
As evident, the limits on the energy dissipations at the all cosmic times
accessible to CMB spectrum investigations (i.e. after the
thermalization redshift)
could be improved by about two order of magnitudes and even
dissipation processes with $\Delta\epsilon/\epsilon_i \sim 10^{-6}$
could be detected and possibly accurately studied.
In particular, it is found that
also the epochs of the two dissipation processes
can be quite well estimated even when
possible imprints from free-free distortions are taken into
account, because such levels of experimental accuracy on a such wide
frequency coverage allow to remove the approximate degeneracy both between
free-free and BE-like distortions and between
Comptonization and BE-like distortions \cite{BS03b}
that remain in presence of future significant improvements
only at $\lambda \gsim 1$~cm or at $\lambda \lsim 1$~cm, respectively.


\begin{table}
\vspace{-1.cm}
\begin{center}
\begin{tabular}{lccccc}
\hline
\hline
\\
Data set & \multicolumn{4}{c}{$(\Delta\epsilon/\epsilon_i)/10^{-7}$} & 
$y_B/10^{-7}$ \\
\cline{2-5}
\\
 & heating at & heating at & heating at &  heating at &free-free dist. at 
\\
 & $y_h=5$ & $y_h=1.5$ & $y_h=0.5$ & $y_h\ll 1$ & $y_h\ll 1$ \\
\hline
\\
F & 414$\pm$1561 & & & -85$\pm$546 & 635$\pm$1531 \\
F & & 353$\pm$1334 & & -88$\pm$560 & 614$\pm$1473 \\
F & & & 286$\pm$1091 & -99$\pm$601 & 583$\pm$1392 \\
F + R & -465$\pm$1056 & & & 163$\pm$436 & -540$\pm$469 \\
F + R & & -418$\pm$922 & & 176$\pm$452 & -542$\pm$459 \\
F + R & & & -343$\pm$789 & 189$\pm$492 & -521$\pm$453 \\
\\
\hline
\\
D + F & -25.6$\pm$56.02 & & & 68.51$\pm$231 & -1.12$\pm$2.64 \\
D + F & & -35.0$\pm$89.1 & &71.6$\pm$240 & -0.67$\pm$1.94 \\
D + F & & & -33.6$\pm$176.4 & 63.5$\pm$275 & -0.14$\pm$1.18 \\
\\
\hline
\\
F-II & -3.43$\pm$13.87 & & & 1.82$\pm$6.20 & -5.22$\pm$12.06 \\
F-II & & -3.05$\pm$12.22 & & 1.92$\pm$6.56 & -5.14$\pm$11.77 \\
F-II & & & -2.64$\pm$10.28 & 2.13$\pm$7.15 & -5.03$\pm$11.24 \\
D + F-II & 0.51$\pm$9.07 & & & 0.36$\pm$4.72 & -0.38$\pm$1.00 \\
D + F-II & & 0.71$\pm$8.00 & &0.20$\pm$4.94 & -0.44$\pm$0.90 \\
D + F-II & & &0.68$\pm$6.85 & 0.10$\pm$5.42 & -0.54$\pm$0.88 \\
\\
\hline
\end{tabular}
\end{center}
\caption{Fits to three kinds of spectral distortions, jontly considered, 
for
different real and/or simulated data.
F: FIRAS; R: recent measures at $\lambda \gsim 1$~cm; D: DIMES;
F-II: FIRAS II.
An underlying BB spectrum is here assumed
for the simulated data sets (see also the text).}
\label{tab_3spec_joint}
\end{table}
%



\begin{table}
\vspace{0.cm}
\begin{center}
\begin{tabular}{lccccc}
\hline
\hline
\\
Data set & \multicolumn{4}{c}{$(\Delta\epsilon/\epsilon_i)/10^{-7}$} & 
$y_B/10^{-7}$ \\
\cline{2-5}
\\
 & heating at & heating at & heating at &  heating at &free-free dist. at 
\\
 & $y_h=5$ & $y_h=1.5$ & $y_h=0.5$ & $y_h\ll 1$ & $y_h\ll 1$ \\
\hline
\\
F & 20$\pm$533 & 25$\pm$453 & 25$\pm$359 & 28$\pm$233 & 272$\pm$920 \\
F + R & 64$\pm$532 & 39$\pm$453 & 28$\pm$359 & 28$\pm$233 &
-455$\pm$424 \\
\\
\hline
\\
D + F & -1.92$\pm$18.12 & -4.5$\pm$38.1 & -3.2$\pm$106.9 &
3.08$\pm$210 & -0.02$\pm$0.88 \\
\\
\hline
\\
F-II & 1.28$\pm$3.95 & 1.06$\pm$3.35  & 0.83$\pm$2.66 & 0.60$\pm$2.08
& -3.26$\pm$7.33 \\
D + F-II & 1.13$\pm$3.85 & 1.02$\pm$3.34 & 0.82$\pm$2.66 &
0.60$\pm$2.08 & -0.07$\pm$0.87 \\
\\
\hline
\end{tabular}
\end{center}
\caption{Fits to a single spectral distortion by considering different 
sets of
real and/or simulated data.
F: FIRAS; R: recent measures at $\lambda \gsim 1$~cm; D: DIMES;
F-II: FIRAS II.
An underlying BB spectrum is here assumed
for the simulated data sets.}
\label{tab_1spec}
\end{table}




\begin{figure}
\vspace{-2.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7.5cm,height=10cm]{dim_fII_bb.ps}&
   \includegraphics[width=7.5cm,height=10cm]{dim_fII_evo.ps}
\end{tabular}
\end{center}
\caption{Left panels: constraints at 95\% CL 
on two energy exchanges at different epochs and on the free-free 
distortion,
jointly considered, as could be
in principle derived by combining a DIMES-like experiment
with a FIRAS~II-like experiment.
An underlying BB spectrum is here assumed.
Solid lines: best fit; dashes: upper and lower limits.
Top-left panel: constraints on
$\Delta\epsilon/\epsilon_i (y_h)$ allowing for
a later energy exchange at $y_h \ll 1$ and for a
free-free distortion.
Middle-left panel: constraints on
$\Delta\epsilon/\epsilon_i (y_h \ll 1)$ allowing for
a previous energy exchange occurring at $y_h$ and for a
free-free distortion.
Bottom-left panel: constraints on
$y_B$ allowing for a first energy exchange occurring at $y_h$
and a second energy exchange at $y_h \ll 1$.
Right panel: comparison between the constraints on the energy exchanges
derived from current measures --
FIRAS and long wavelength data -- (dotted lines;
in practice FIRAS data alone set the current constraints),
from FIRAS data jointed to
a simulated data set from a DIMES-like experiment
(dash-dotted lines),
and, finally, from simulated data sets from a DIMES-like experiment
jointed to a FIRAS~II-like experiment (dashed lines).
An underlying BB spectrum is here assumed
for the simulated data sets.
In the first two cases (dotted lines and dash-dotted lines)
we report the constraints on
$\Delta\epsilon/\epsilon_i (y_h)$ allowing for
a later energy exchange at $y_h \ll 1$ but neglecting
free-free distortions (i.e. assuming $y_B =0$).
In the last case (dashed lines) we relax the
assumption $y_B =0$, i.e. we jointly consider
three kinds of spectral distortions.}
\label{constr_bb}
\end{figure}
%

\subsection{Probing the baryon density with the CMB spectrum?}
\label{subsec:baryons}

In presence of an early distortion,
$\Ohat_b$ could be in principle estimated by CMB spectrum observations 
at long wavelengths, able to detect the wavelength of 
the minimum of the absolute temperature,
determined only by the well known physics of the radiative
processes in an expanding universe during the radiation dominated era.
For distortions at relatively high redshifts ($y_h \gsim 1$),
the value of $\Ohat_b$ can be simply determined by
the knowledge of the frequency position of the minimum of
the CMB absolute temperature
\cite{DD80, BDD91a}:

\begin{equation}
\lambda_{m, BE} \simeq 41.56 \left(\frac{\Ohat_b}{0.05}\right)^{-2/3}\,\hbox{cm} \, .
\label{eq:lmin}
\end{equation}

\noindent
For dissipations at $y_h \gsim 5$,
the amplitude of this temperature decrement is 
\cite{DD80, BDD91a}:

\begin{equation}
\Delta T_m \simeq 1.17\times10^{-3}\left(\frac{\mu_0}{10^{-5}}\right)
\left(\frac{T_0}{2.725\,\mbox{K}}\right)
\left(\frac{\Ohat_b}{0.05}\right)^{-2/3}\,\mbox{K} \, ,
\label{eq:dTb}
\end{equation}

\noindent
where $\mu_0$ is the chemical potential at the redshift $z_1$ corresponding
to $y_h=5$.
Eq.~(\ref{eq:lmin})
gives the range of wavelengths to observe
for a firm evaluation of $\Ohat_b$. As example,
for $\Ohat_b \sim 0.05$ we need to accurately measure the CMB
absolute temperature up to wavelengths of about 50~cm, clearly out from
the DIMES range. 

Accurate simulations carried out even in the ``best'' work condition
in which very accurate measures (at $\approx$~FIRAS~II level)
at $\lambda \lsim 1$~cm are used to determine the
chemical potential and longer wavelengths to estimate
$\Ohat_b$ through the decreasing of the equivalent thermodynamic
temperature at increasing wavelengths,
confirm the above simple result: given the current limits on the chemical
potential, only high accuracy measures 
(at $\approx$~DIMES level) up to very long
wavelengths ($\approx 50$~cm, about the minimum of the
equivalent thermodynamic temperature) are able to provide
a firm and accurate independent cross-check on $\Ohat_b$,
comparable to that based on CMB anisotropy experiments.

On the contrary, just the very weak dependence 
of the distorted spectra at $\lambda \lsim 15$~cm 
on $\Ohat_b$
implies that the
constraints on $y_B$ and on $\Delta\epsilon/\epsilon_i$ as function of $y_h$
(at $y_h \lsim 5$) 
achievable with DIMES and FIRAS~II depend only very weakly 
in explicit way on the assumed baryon density
(while, of course, those on $\Delta\epsilon/\epsilon_i$ as function of
$z_h$ depend $\Ohat_b$ -- see Eq.~(\ref{eq_y_e})).


\section{PROBING THE REIONIZATION OF THE UNIVERSE}
\label{sec:reionization}

The accurate understanding of the ionization history of the universe
plays a fundamental role in the modern cosmology.
The classical theory of hydrogen
recombination for pure baryonic cosmological models
%Peebles - Zel'dovich, Kurt and Sunyaev   
\cite{peebles, zeldovich}, 
subsequently extended to non-baryonic dark matter models 
%Zabotin and Naselsky  -  Jones and Wyse  - Seager, Sasselov and Scott -
% Peebles, Seager and Hu
\cite{zabotin, jones, recfast, psh}
can be modified in various ways to take into account
additional sources of photon and energy production
able to significantly
increase the ionization fraction, $x_e$,
above the residual fraction ($\sim10^{-3}$)
after the standard recombination epoch
at $\zrec\simeq 10^3$.
These photon and energy production processes may leave imprints
in the CMB providing a crucial ``integrated'' information on the so-called
{\it dark} and {\it dawn} {\it ages}, i.e. the epochs
before or at the beginning the formation of first stars and primeval galaxies,
complementary to those obtained by the study of the diffuse backgrounds
in other frequency bands and that are impossible or difficult to 
study with other direct astronomical observations.

\subsection{WMAP results}
\label{subsec:wmap_res}

Among the extraordinary results recently achieved by WMAP
the detection of a cosmological reionization at relevant 
redshifts represents one of the new most remarkable
discovery of the recent years. 
In spite of the uncertainty associated to the degeneracy
\cite{bondetal_deg} between the Thomson scattering 
optical depth, $\tau$, and 
the spectral index of primordial perturbation, $n_s$,
in CMB anisotropy data,  
a cosmological reionization at substantial 
redshifts is supported 
by the decrease of the temperature
angular power spectrum at high multipoles 
and by an excess in the
TE cross-power spectrum on large angular scale
(multipoles $\ell \lsim 7$) with respect to models
with no-reionization or reionization with quite low ($\sim 0.05$) values
of $\tau$.
According to WMAP, the favourite values of $\tau$ are $\gsim 0.1$, 
with a current best fit of $\simeq 0.17$ based on the combination of WMAP with 
additional CMB anisotropy data at higher resolution and 
other kinds of astronomical observations (see, e.g.,
\cite{PBM_NA}).
On the other hand, 
the details and the physical 
explanation of the cosmological reionization 
are still unclear. 

Since the WMAP detection of the reionization
at substantial redshifts, many models have been 
proposed and/or reconsidered to account for the measure 
of $\tau$ (see, e.g., \cite{bean}; see also 
Sect.~\ref{subsec:spec_dist_mod}).
Certainly, a significant contribution 
($\simeq 0.05-0.07$) to the value of $\tau$ 
derives from the ionization, 
likely associated to photon production
and hot gas ejection by primeval galaxies and quasars,
at relatively low redshifts ($z \lsim \zreio^{(2)} \simeq 5-7$) 
where direct observations of the Gunn-Peterson effect
in quasars probe a high ionization level of the intergalactic medium.
The remaining contribution ($\simeq 0.05-0.12$) to the observed value 
of $\tau$ should be provided by processes at higher redshifts.
Although uncertain because of the possible non-uniformity 
of the ionization of the intergalactic medium,
the indication of an increase of the Ly$\alpha$ opacity 
for Gunn-Peterson tests toward some quasars at $z \sim 6$
\cite{becker, fan}
combined to the large WMAP value of $\tau$
suggests the possibility of a twice reionization, the first one
at relevant redshifts, $\zreio^{(1)}\simeq 15$, possibly associated
to Population III stars \cite{cen2003}, or even at higher redshifts,
$\zreio \gsim some \times 10$, in models involving 
a relevant photon production by particle decay, 
matter-antimatter annihilation, or black-hole evaporation
and so on, followed by the subsequent 
reionization at $z \simeq \zreio^{(2)} \simeq 6$. 

The reionization imprints on the CMB 
can be divided in three categories: $i)$ decreasing of the power
of CMB temperature anisotropy at large multipoles
because of photon diffusion, $ii)$ increasing
of the power of CMB polarization and temperature-polarization
cross correlation anisotropy at all multipoles with relevant
features possibly more remarkable at low and middle multipoles 
according to the reionization epoch
because of the delay of the effective last scattering surface, 
$iii)$ generation of CMB Comptonization and free-free spectral distortions 
associated to the heating of the electron temperature of the 
intergalactic medium during the reionization epoch.
The imprints on CMB anisotropies are mainly dependent 
on the ionization history while 
CMB spectral distortions strongly depend 
also on the thermal history. 
It is therefore interesting in the context of this review 
to analyse the sensitivity of future CMB anisotropy and spectrum
space experiments to the imprints left from different 
reionization scenarios
and to their possible capabilities to distinguish among
different models under quite general conditions.
In the next two sections we discuss this topic by adopting a   
phenomenological description of the reionization process
able to account in a simple parametric form 
various scenarios occurring a very different cosmic times. 

\subsection{Simple phenomenological models: polarization anisotropies}
\label{subsec:reion_phen_mod_pol}

The reionization process 
can be described phenomenologically in terms of injection of
additional ionizing photons 
%via the approach by 
%Peebles, Seager and Hu  -  Doroshkevich and Naselsky - Doroshkevich etal 
\cite{psh, dn, dnnn}.
The ionization
fraction of matter, $x_e=n_e/\overline{n}$, can be obtained
from the balance between the processes of recombination and ionization:
\begin{equation}
\frac{dx_e}{dt}=-\alpha_{\rm rec}(T) \nb x^2_e +
\varepsilon_{i}(z) (1-x_e) {{H}}(z),
\label{eq3}
\end{equation}
where 
$\nb(z)$ is and the mean baryonic density at the redshift $z$,
$T$ is the temperature of the plasma, 
$\alpha_{\rm rec}(T)\simeq 4\times 10^{-13} \left(T/10^4
K \right)^{-0.6} {\rm s}^{-1}{\rm cm}^{-3}$ is the recombination coefficient, 
and $\varepsilon_{i}(z)$ is the efficiency of the  
ionizing photon production giving 
the ionizing photon production rate 
%\begin{equation}
${dn_i}/{dt}=\varepsilon_{i}(z) \nb(z) {{H}}(z) \, .$
%\label{eq2}
%\end{equation}

\noindent
The choice of the function $\varepsilon_{i}(z)$
allows to model the ionization history
also in the presence of extra sources of ionizing photons
(e.g. Ly-$\alpha$ and ionization photons from 
primavel stars, galaxies, and active galaxies, or from 
primordial black hole decays, electromagnetic cascades from particle 
release from topological defects or decay of super heavy dark matter, 
...).  

Assuming equilibrium 
between the recombination and the ionization process, 
for any given history of the plasma temperature 
the evolution of the ionization fraction
is given by the solution of the simple second order equation
obtained by the equality ${dx_e}/{dt}=0$. 

For late processes, a simple expression  
describing a first reionization at relevant redshifts
followed by a second reionization, 
possibly mimicking the model by Cen \cite{cen2003}, 
has been proposed~\cite{nc03} in the form:

\begin{equation}
\varepsilon_{i}(z)= \varepsilon_{0} \exp
\left[-\frac{(z-\zreio^{(1)})^2}{(\Delta z_1)^2}\right]
+\varepsilon_{1}(1+z)^{-m}\Theta(\zreio^{(1)}-z) \, ;
\label{eq5.0}
\end{equation}
here $\varepsilon_{0}$,
$\zreio^{(1)}$, and 
$\Delta z_1\ll \zreio^{(1)}$ are free
parameters describing the history
of the first epoch of reionization
which significantly decreases at $z > \zreio^{(1)}$;
$\varepsilon_{1}$, $m$, and (again)
$\zreio^{(1)}$ are free
parameters describing the history
of the second epoch of reionization
resulting into a increasing of 
$\varepsilon_{i}(z)$ with the time,
being $\Theta(x)$  the step function.

Although quite weakly in this modelization, because of the dependence
on the temperature as a power of $\simeq -0.6$
of the recombination coefficient, 
the thermal history influences the ionization fraction
evolution. By using the
matter temperature evolution
$T(z)\simeq 270 \left(1+z/100 \right)^2 {\rm K}$
and modifying the ionization history 
in the {\sc cmbfast} code, 
the CMB angular power spectrum, in both temperature
and polarization, has been computed \cite{nc03} for some representative choices 
of the above free parameters.
As shown by Fig.~\ref{nas_ch_late}
for the case of the E-mode polarization power spectrum,
the differences between different late reionization scenarios
associated to very different parameters are of particular interest
at relatively low multipoles. 
Provided that the contribution from the Galactic foregrounds,
particularly relevant at these multipoles, could be accurately
modeled, the difference between a scenario involving a single 
reionization at $z \simeq \zreio^{(2)}$ and 
scenarios involving a twice reionization could be
detected by the {\sc Planck} polarization accuracy.

\begin{figure}[t]
%\vspace{-1.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7cm,height=7cm]{nc3.eps}&
   \includegraphics[width=7cm,height=7cm]{diffcen.eps}
\end{tabular}
\end{center}
\caption{Left panel: polarization (E-mode) angular power spectrum for
late reionization models.
The dash and dash-dot lines correspond to models with a single full
reionization starting at $z \simeq 6$ (a) and at $z \simeq 13.6$ (b), respectively;
the solid and dotted lines correspond to the model described by 
Eq.~(\ref{eq5.0}) assuming
$\varepsilon_{0} = 1.3 \times 10^3$, $m=7$ and, respectively, 
$\varepsilon_{1}=10^9$ (c) and $10^8$ (d).
Right panel: relative differences between the power spectra shown
in the left panel compared to {\sc Planck} relative sensitivity  
(the analogous of Eq.~(\ref{fullvariance}), but for the E-mode;
$f_{sky}=0.65$)
with no multipole binning (thick dashes) and with a suitable
multipole binning (thick solid line). 
Solid line: model (d) minus model (c); dash-dot line: 
model (b) minus model (c); dash line: model (a) minus model (c)
(with MNRAS permission, courtesy 
of P.~Naselsky and L.-Y.~Chiang).}
\label{nas_ch_late}
\end{figure}

Models involving a substantial reionization at redshifts, 
$z \simeq \zreio$, much higher than $\zreio^{(1)} \sim 15$
can not be excluded by current data.
A Gaussian parametric form 

\begin{equation}
\varepsilon_{i}(z)= \xi
\exp \left[-\frac{(z-\zreio)^2}{(\Delta z)^2}\right] \, ,
\label{eqc9}
\end{equation}

\noindent
quite similar to that assumed to describe 
the first reionization epoch for late processes,
can be exploited in this context \cite{nc03};
again $\xi$, $\zreio$, and 
$\Delta z$ are free
parameters describing the history
of this high redshift reionization scenario.
Assuming $\Delta z \ll \zreio$ implies the choice 
of a peak-like model.
Again, it is necessary to add the evolution of the matter 
temperature which should peak at typical values 
of $T_p \approx (1-2) \times 10^4$~K. 
In \cite{nc03} it is assumed an extremely short heating phase 
($\delta$-like) about $\zreio$. After the end of the heating phase
the matter temperature is determined by the usual equation
for the electron temperature evolution, dominated, at high redshifts,
by the Compton cooling term. Therefore a set of 
two differential equations, one  
for the ionization fraction and the other for the matter temperature,
describe the problem~\footnote{Simple approximate analytical solution 
can be used in the limit $\xi \ll 1$. We find also that 
the the system can be easily solved through a numerical integration. 
A simple backward differential scheme with a very small time 
step compared to the other relevant timescales does not introduce 
relevant errors in this context.}. 
This modified ionization history has been 
included in the {\sc cmbfast} code to  
computed the CMB angular power spectrum, in both temperature
and polarization, for some representative choices 
of the above free parameters.
As shown by Fig.~\ref{nas_ch_early}
for the E-mode polarization angular power spectrum,
the differences between different early reionization scenarios
associated to different parameters 
and between them and a scenario involving a single late
reionization at $z \simeq \zreio^{(2)}$
are relevant at low and also at middle multipoles, 
$\ell \sim few \times (10-100)$. 
This is of particular interest in the light of the 
{\sc Planck} polarization accuracy in the 
multipole region of the CMB acoustic peaks
where the contribution from the Galactic foregrounds
is expected to significantly decrease with respect to the level 
it has at low multipoles.

\begin{figure}[t]
%\vspace{-1.5cm}
\begin{center}
\begin{tabular}{cc}
   \includegraphics[width=7cm,height=7cm]{nc33.eps}&
   \includegraphics[width=7cm,height=7cm]{nc34.eps}
\end{tabular}
\end{center}

\caption{Left panel: polarization (E-mode) angular power spectrum for
early peak-like reionization models.
The dotted line corresponds to the model with a single full
reionization starting at $z \simeq 6$ (a);
the dash, the solid, and the dash-dott lines correspond 
to the model described by 
Eq.~(\ref{eqc9}) assuming
$\zreio =500$, $\Delta z =12.5$
and, respectively, 
$\xi= 100$ (b), 10 (c), and 1 (d).
Right panel: relative differences between the power spectra shown
in the left panel compared to {\sc Planck} cosmic variance limit
($f_{sky}=0.65$, thick dotted line; $f_{sky}=1$, thick solid line).
Solid line: model (b) minus model (a); dash line: 
model (c) minus model (a); dash-dot line: model (d) minus model (a)
(with MNRAS permission, courtesy 
of P.~Naselsky and L.-Y.~Chiang).}
\label{nas_ch_early}
\end{figure}


\subsection{Simple phenomenological models: spectral distortions}
\label{subsec:reion_phen_mod_spec}

The relevance of the detection of spectral distortions 
has been partially renewed 
\cite{KOG03}
by the WMAP satellite discovery of a
reionization phase at relevant redshifts.

The computation of the CMB spectral distortions associated to 
the reionization parametric model presented in the 
previous section is strictly related to the detailed description 
of the thermal history.

For the late processes,   
we assume here a matter thermal history similar to that reported 
by Cen \cite{cen2003}: a matter temperature $T$ in approximate thermal equilibrium with the 
radiation field (i.e. equal to $T_0 (1+z)$) at $z \gsim 27$;
a linear dependence of ${\rm log} T$ on $z$ at subsequent times
to reach a temperature $T^{(1)}$ (assumed here $1.5 \times 10^4$~K
for numerical estimates) at $z=\zreio^{(1)}$, kept then constant 
up to $z=\zreio^{(2)}$ when it rapidly increases up to
a temperature $T^{(2)}$ (assumed here $2 \times 10^4$~K
for numerical estimates) kept then constant up to low redshifts.   

We have implemented this thermal history in the 
equilibrium evolution of the 
ionization fraction and then used 
these thermal and ionization histories to 
compute the Comptonization and free-free distortions
as described in \cite{BDD95} 
by generalizing the code to include also the case of a $\Lambda$CDM model
(see also Sect.~\ref{spec_th_fram}).

In Fig.~\ref{late_all} we report our 
contour plot results for
the optical depth $\tau$ and the fractional energy injection
associated to the Comptonization distortion 
as functions of the free parameters   
$\beta=\varepsilon_{1}/10^9$ and $m$,
by separately showing for $\Delta \epsilon / \epsilon_i$ 
the results of the integration up to
$z=0$ and up to $z=5$ (of course, the difference 
between these results gives the fractional energy injected
in the plasma at $z \le 5$). For simplicity, we report here
the results for an interval of $\beta$ and $m$ producing values of $\tau$ 
close to the WMAP best fit. 
Although a detailed computation requires to take into account
the dependence of the ionization history on the matter temperature 
evolution, these results can be approximately 
rescaled to different values of $T^{(1)}$ and $T^{(2)}$ by considering 
the linear dependence of the Comptonization parameter on $T$. 
By comparing the results of Fig.~\ref{late_all} 
with the sensitivities reported in Table~\ref{tab_3spec_joint},
it is clear that the predicted Comptonization
distortions could detected and possibly measured by 
an experiment with a sensitivity like that of FIRAS~II.
Analogously to the case of the polarization anisotropy signatures,
the difference between the Comptonization distortions by 
models involving a twice reionization (or a 
continuous reionization starting at 
$z \simeq \zreio^{(1)}$)
and models with a single reionization at $z \simeq \zreio^{(2)}$
is comparable or above the FIRAS~II sensitivity.
The free-free distortion parameter $y_B$ results to be too small,
well below the DIMES sensitivity, and is not reported here.

\begin{figure}[t]
\vspace{-1.5cm}
\begin{center}
\epsfig{file=vedi_late_all.ps,width=16.cm}
\end{center}
\vspace{-7cm}
\caption{Contour plots of the optical depth and 
of the fractional injected energy associated to the Comptonization parameter
as functions of $\beta$ and $m$ 
in the case of late reionization processes.
Left panel: $\tau$
evaluated by integrating up to $z=0$.
Middle and right panels: $\Delta \epsilon / \epsilon_i \simeq 4u$ 
(in units of $10^{-6}$)
computed by integrating up to $z=0$ and up to $z=5$,
respectively.}
\label{late_all}
\end{figure}

For the study of the spectral distortions 
associated to early peak-like reionization processes,
we have numerically integrated the differential equations 
for the ionization fraction and the matter temperature
as described in the previous section.
Differently from 
the $\delta$-like assumption 
for the matter temperature during the heating phase
about $\zreio$ (that is not particularly critical 
for polarization anisotropy considerations)
we adopt here a Gaussian parametric form 

\begin{equation}
T(z)= T_p \exp \left[-\frac{(z-\zreio)^2}{(\Delta z)^2}\right] \,  
\label{eqc9_T}
\end{equation}

\noindent
for the matter temperature during the heating phase
(within a redshift interval $\simeq \pm 3 \Delta z$
about $\zreio$) and then assume the usual 
temperature evolution equation, dominated by the  
Compton cooling term, at later epochs
($T_p = 1.5 \times 10^4$~K 
and $\Delta z = 0.025 \zreio$
are adopted here for numerical estimates).
It is in fact quite reasonable to assume a similar
time dependence for both the efficiency of the  
ionizing photon production, $\varepsilon_{i}(z)$, 
and the matter temperature during the active phase.
We assume as initial conditions 
at the beginning of the heating/ionization phase
the thermal equilibrium between matter and radiation
and the residual ionization fraction obtained 
at the considered redshift from the standard 
recombination.

Finally, we have implemented the thermal and ionization history
as described above in the code \cite{BDD95} 
for the computation of the Comptonization and free-free distortions.

In Fig.~\ref{early_all} we report our 
results in terms of contour plots
for the optical depth $\tau$ and the fractional energy injection
associated to the Comptonization distortion 
as functions of the free parameters   
$\xi$ and $\zreio$. These results can be 
rescaled to different choices of 
$T_p$ and $\Delta z$ by using the approximate
proportionality relations between  
$\tau$ and $\Delta z$  and between
$u$ and $T_p \Delta z$~\footnote{In reality, 
for the lowest considered values of $\xi$ ($\xi \approx 1$) 
we find an increasing 
of the Comptonization distortion with 
$\Delta z$ larger by a factor $\approx 1.5-3$
than that suggested by the above proportionality and
related to the different initial conditions 
(the process starts at earlier times) 
and to the different coupling between 
the ionization fraction and the matter temperature.
We find that this holds also for the free-free
distortion parameter $y_B$.}.
Fig.~\ref{early_all} shows that a large region 
of the $\xi$ and $\zreio$ parameter space
can be clearly ruled out by current WMAP data
because of the violation of the limits 
on the optical depth. It is also remarkable
that in the permitted region of $\xi$ and $\zreio$ 
(corresponding to $\tau \sim 0.1$) the model 
predicts values of fractional injected energy 
$\Delta \epsilon / \epsilon_i \simeq 4u \sim 10^{-6}$,
again in principle measurable with the FIRAS~II sensitivity.
We find again values of free-free distortion parameter $y_B$ too small
with respect to the DIMES sensitivity~\footnote{By considering
higher matter temperature values (up to $6 \times 10^4$~K),
we find only a weak dependence of $y_B$ on $T_p$ 
because the typical decreasing of $y_B$ with $T_p$ is approximately
compensated by the increasing of the ionization fraction
because of the decreasing of the recombination efficiency.}. 
 
To summarize, since it is plausible 
to assume peak matter temperatures $\gsim (1-2)\times 10^4$~K 
to have an efficient (late or early) reionization,
values of 
$\Delta \epsilon / \epsilon_i \simeq 4u \sim (1-2) \times 10^{-6}$
should be considered as typical (lower limit) predictions 
for the Comptonization distortion associated to reionization 
scenarios compatible with the WMAP results.

%
\begin{figure}
\vspace{-1.5cm}
\begin{center}
\epsfig{file=vedi_early_all.ps,width=14.cm}
\end{center}
\vspace{-7cm}
\caption{Contour plots of the optical depth, $\tau$,
(left panel) 
and of the fractional energy injection 
associated to the Comptonization parameter, 
$\Delta \epsilon / \epsilon_i \simeq 4u$, 
(right panel)
as functions of $\xi$ and $\zreio$
in the case of early peak-like reionization processes (logarithmic scale).}
\label{early_all}
\end{figure}

\subsection{Late spectral distortions from some specific models} 
\label{subsec:spec_dist_mod}

In the previous section 
we have computed the optical depth and the free-free and Comptonization
distortions predicted on the basis of a phenomenological model
and the constraints on them that could be
set by the new generation of CMB spectrum experiments 
without assuming detailed physical models for their genesis.
Such kinds of late distortions are expected in many astrophysical
scenarios involving some energy dissipation mechanisms
during various stages of the star and galaxy evolution
or some particle or scalar field decay model
(see e.g. \cite{DB92, TS95}).

Without the ambition to exhaustively cover a so wide topic,
we compare here the coupled free-free and Comptonization distortions
for some of the models recently discussed in the literature, 
possibly in the context of the high reionization optical depth 
detected by WMAP, and discuss the possibility to reveal them with the
new generation of CMB spectrum experiments.

\subsubsection{Free-free emitters}
\label{freefreeemitters}

Oh \cite{OH99} predicted the level of free-free distortion
can be produced by ionized halos in the early stage of galaxy formation
by computing the moments of the intensity distribution
from a Press-Schechter based model.
The predicted free-free distortion results to be
$\Delta T_{B}=3.4\times 10^{-3}$~K
at $\simeq 2$~GHz corresponding to a free-free distortion parameter
$y_{B}\simeq 1.5\times 10^{-6}$,
%$y_{B}\simeq 1.548\times 10^{-6}$,
well within the observational capability of DIMES.
The associated Comptonization distortion predicted in this work
is below the current FIRAS upper limit by about one order of magnitude,
and is then likely measurable by a FIRAS~II-like experiment.
Moreover, this work assumed that free-free emitters are
the only radio-bright sources in the sky.
The existence of radio-loud galaxies and AGNs is likely to increase the
levels of these kinds of CMB spectral distortions.

\subsubsection{Quasar driven blastwaves}
\label{blastwaves}

In the presence of significant outflows, the energy content of the inner
regions of quasars and other classes of active galaxies could be transfered
to the intergalactic medium, possibly through shock wave fronts, contributing
to the reionization at late epochs ($z \lsim \zreio^{(2)}$) and producing
spectral distortions. 

The integrated Comptonization distortion from quasar driven
blastwaves has been recently computed by Platania et al. \cite{platania}
through a quite general ``energetic'' approach, not particularly
related to a detailed physical assumption. They found
$u \approx 2.4 \times 10^{-6}$, clearly measurable
with a FIRAS~II-like experiment, with approximately
the same fractional contribution from low-$z$ (0--2) and high-z (2--4)
objects. The evaluation of the corresponding integrated free-free
distortion is less model independent, being significantly sensitive
to the density profile inside the blastwave because of the
$n^2_e$ dependence of the free-free emission. By assuming the model
described in Sect.~2 of \cite{platania},
it is possible to compute \cite{BS03b} the ratio between the 
Comptonization parameter $u$
and the free-free parameter $y_B$ integrated over the
line-of-sight of the blastwave centre between the galaxy outer cut-off
radius, $R_g$, approximately separating the virialized and infall regions,
and an inner radius, $r_{ff}$ [$\approx (1/10 - 1/20) \times R_g$],
where the time required for the shock front
to reach the outer radius of the galaxy equals the free-free cooling
timescale (it is in fact reasonable to assume that the physical conditions
at $r<r_{ff}$ are more related to the central engine than to the
blastwave evolution). By assuming an electron temperature
$T_e \sim 10^6$~K ($T_e \sim 10^7$~K)
and a wide range of line-of-sight velocity
dispersions, $\sigma \sim 100-400$~Km/s,
we find $y_B/u \lsim {\rm few} \times 10^{-2}$
($\lsim {\rm few} \times 10^{-3}$) for
objects both at $z \sim 1$ and at $z \sim 3$, while only for
low values of $T_e$ ($\sim 10^5$~K) and high values of $\sigma$
($\sim 400$) $y_B/u$ approaches the unity. A reasonable
upper limit to $y_B$ in this model is then
$\sim {\rm some} \times 10^{-8} - 10^{-7}$,
a value significantly smaller than the free-free distortion
predicted in the model by Oh \cite{OH99}
and below or comparable to the sensitivity
of a DIMES-like experiment.

\subsubsection{First stars in galaxies}
\label{firststars}

The reionization of the universe indicated by the WMAP data
must have begun at relatively high redshift.
Ciardi, Ferrara and White \cite{CFW03} have  studied the reionization
process using supercomputer simulations of a large and representative 
region of
a universe which has cosmological parameters consistent with the WMAP
results. The simulation follows both the radiative transfer of ionizing 
photons
and the formation and evolution of the galaxy population which produces 
them.

They have shown that the WMAP measured optical depth to electron
scattering is easily reproduced by a model in which reionization is caused 
by
the first stars in galaxies with total masses of a few 
$\times10^9\;\Msun$.
Moreover, the first
stars are ``normal objects'', i.e. their mass is in the range 1--50
$\Msun$, but metal-free. Among the different model explored, the ``best''
WMAP value for $\tau_e$ is matched assuming
a moderately top-heavy initial
mass function (IMF) (Larson IMF with $M_c=5\;\Msun$)
and an escape fraction of 20\%. A Salpeter IMF with
the same escape fraction gives $\tau_e=0.132$.
Decreasing $f_{esc}$ to 5\% gives $\tau_e=0.104$,
which disagrees with WMAP only at $\simeq 1.0 - 1.5 \sigma$ level,
the exact level depending on the detailed cosmological scenario adopted to 
fit the WMAP
(and auxiliary) data.

Using the redshift evolution of the density of free electrons obtained by
these simulations (kindly provided us by A. Ferrara), we compute the 
expected CMB
spectral distortions. We obtain $u-$distortions of the order of
$2.3\times10^{-6}$ ($4.5\times 10^{-7}$) for a constant electron 
temperature
of $10^{6}$~K ($2\times 10^{4}$~K) corresponding to an energy injection of
$\Delta\epsilon/\epsilon_i\sim 9.2\times 10^{-6}$ ($1.8\times 10^{-6}$)
well below the current FIRAS upper limits, but easily detectable by
an experiment with a sensitivity such that proposed for FIRAS II.
We compute also the corresponding
free-free distortion that results to be so small ($y_B\sim 10^{-11}$)
that can not be detected by any future experiment.

In the best-fit model of Ciardi, Ferrara, and White \cite{CFW03} 
reionization is essentially
complete by $z_r\simeq 13$. This is difficult to reconcile with 
observations
of the Gunn-Peterson effect in $z>6$ quasars \cite{becker, fan}.
This implies a volume-average neutral fraction above
$10^{-3}$ and a mass-averaged neutral fraction $\sim 1$\% at $z=6$.
An intriguing possibility
is that the universe was reionized twice \cite{cen2003, WhLo03} 
with a relatively short redshift interval in which the IGM became neutral 
again.


\subsubsection{Particle decays}
\label{particledecays}

The models discussed above, related to astrophysical processes,
could be probed also through dedicated astronomical observations
and/or through the analysis of the corresponding imprints left as 
(frequency dependent) foreground fluctuations.

Alternative scenarios involve particle decays.
In this context, the possible role of radiative decays 
of massive particles has been recently 
reconsidered \cite{Kasuyaetal03}.
A different model has been proposed 
in a recent work \cite{HansenHaiman2003} where
it is considered the case of a particle which
decays around a redshift $z\sim 20$ into electron/positron pairs.
The decay products
could have energies high enough to reionize the light elements. If this
hypothetical particle is sufficient abundant, then it may explain the high
value of the optical depth, without the need for stars to reionize the
universe at high redshift, but normal stellar populations could form at
$z\simlt 10$ with the usual efficiencies and account for the completion of
reionization epoch that appears to be occurring at $z<10$.
The authors proposed that this particle could be a sterile 
neutrino with a mass $m_\nu\sim 200$~MeV and decay time $\tau_d \sim 4\times 
10^{15}$~s.
The decaying of this neutrino can account for the electron scattering 
optical depth $\tau\simeq 0.16$ \cite{kogutetal03} 
without violating existing astrophysical limits on the CMB and gamma ray 
background.
In particular, the authors have shown that the expected energy injection in the 
CMB
from this process is $\Delta\epsilon/\epsilon_i\sim (0.4-3) \times 10^{-6}$, 
depending
on the fraction of the mean electron energy that goes into heating the 
IGM.
These values are well below the current FIRAS upper limits, but in 
principle
can be detected by future experiments such as FIRAS~II. 
Estimates of the associated free-free distortion 
generated during a redshift interval corresponding
to a time interval between $\sim \tau_d /10$ and $\sim 3 \tau_d$
can be easily computed for different simple thermal histories 
($T_e \simeq {\rm const}$
or $\phi_e \simeq {\rm const}$) producing the above values of
$\Delta\epsilon/\epsilon_i$. The expected $y_B$ is in the
range $(0.4-1.4) \times 10^{-7}$ depending mainly on the exact amount of 
energy
that goes into the IGM and only slightly on the considered thermal history 
of the
process~\footnote{Note the difference with respect the results 
based on the phenomenological models described 
in Sect.~\ref{subsec:reion_phen_mod_spec} (that produce smaller 
values of $y_B$) due to the longer process duration
assumed in this case.}.
Particularly for cases in which a large amount of the electron
energy goes into heating the IGM,
this distortion can be in principle observable
by a future experiment like DIMES.

\subsubsection{Summary of observational chances}
\label{summaryobs}

Table~\ref{tab_reionproc}
summarizes the chances of observing the Comptonization
and free-free distortions for the four classes of processes
discussed in this section on the basis of the
sensitivities reported in Table~\ref{tab_3spec_joint}
(of course, a more optimistic
conclusion for the possibility to measure the Comptonization
distortion, i.e. a sensitivity improvement by a factor $\simeq 2.5-3$
practically identical to that reported in 
Table~\ref{tab_1spec} because of the very different frequency location of 
free-free and Comptonization signatures,
could be derived by assuming a quite strong prior
on the earlier energy exchange).

\begin{table}
\begin{center}
\begin{tabular}{lccccc}
\hline
\hline
\\
Process & Comptonization distortion & Free-free distortion \\
        & (mainly through FIRAS~II) & (mainly through DIMES) \\
\hline
FFE     & measurable          &  measurable \\
\hline
QSOB    & measurable                & $\approx$~at limit \\
\hline
FSG     & measurable                & unobservable \\
\hline
PD      & measurable                & observable  \\
\hline
\end{tabular}
\end{center}
\caption{Chances to observe or quite accurately measure Comptonization and
free-free distortions with the new generation of CMB spectrum space 
experiments
for some classes of processes.
FFE: free-free emitters; QSOB: quasar driven blastwaves;
FSG: first stars in galaxies; PD: particle decay.
Clearly, the combined effect of these (and, of course, many
others) processes should be carefully evaluated and,
at least for the astrophysical models,
the ``integrated'' information contained in the CMB spectrum
should be hopefully complemented by
(or, viceversa, should complement the)
dedicated observations (or, at least, detections)
of the corresponding astrophysical
sources and, possibly, foreground fluctuation analyses.
Anyway, these examples show how the combined information of
accurate CMB spectrum measures at short and long
wavelengths can greatly improve the reliability
of a physical explanation of a possible observation
of a given kind of spectral distortion.}
\label{tab_reionproc}
\end{table}



\section{DISCUSSION}
\label{sec:disc}

Since its discovery, the CMB played a crucial role
for the understanding of the universe structure and evolution.
After the first decade of studies, the space has been clearly recognized
as the best laboratory to measure 
the fundamental properties of this background.
Two successful space missions, COBE and WMAP, allowed to 
firmly establish the cosmological origin of the microwave background
through its spectral shape, in strict agreement with a blackbody 
within the accuracy, and the detection of the large scale anisotropy,
and made the CMB a precise laboratory for the determination 
of the main cosmological parameters through
the accurate measure of the CMB anisotropy angular power spectrum
on a wide multipole range.

Excellent ground-based and balloon-borne 
anisotropy experiments as well as radio 
interferometric facilities are currently on-going and 
planned for the future, and they will allow to study with an extreme 
sensitivity the CMB anisotropy at small scales.
In particular, ground-based observations will play a major role in 
the mapping of secondary anisotropies at very small angular scales, 
corresponding to multipoles $\ell \ge few \times 10^3$, related to the 
non-linear stages of the evolution of the structures 
in the universe. 

On the contrary, space missions offer the unique 
opportunity for a clean and accurate joint study of the CMB anisotropies  
with a wide frequency coverage 
from large angular scales to few arcminute scales, 
where the non-linear effects, although non negligible, 
%(see e.g. Sect. \ref{sec:hdm}), 
do not superimpose significantly to the primordial 
imprints.
In this respect, WMAP opened a new phase in the CMB cosmology,
the so-called ``high precision cosmology''.
On the other hand, the understanding of many of the cosmological 
problems, some of them just opened by WMAP,
need a further step: a better subtraction of foregrounds,
achievable only with a wider frequency coverage, a better accuracy
at intermediate multipoles, and the capability to accurately measure
the CMB angular power spectrum, both in temperature and in polarization,
up to multipoles $\ell \sim few \times 10^3$, or in other words,
a detailed imaging of the primordial CMB anisotropies.
The {\sc Planck} satellite will represent
the major effort in this direction.
We have discussed some topics of particular 
relevance in the light of the {\sc Planck} scientific objectives. In fact, 
{\sc Planck}  will allow to reveal the imprints from gravitational waves, 
a crucial probe for the inflation. A wide set of cosmological parameters
for a wide set of cosmological scenarios will be accurately measured
by minimizing the use of auxiliary informations.
In particular, this will allow to define the contribution of 
the different kinds of dark matter to the density of the universe 
and to constrain the physical properties of the unknown 
constituents of the $\simeq 95$\% of the universe energy density, 
from the still poorly understood properties
of dark matter to the unknown dark energy. 
The statistical properties 
of the primordial seeds of the structures observed in the
universe will be accurately constrained. 
The others branches
of the observational and theoretical cosmology will have then 
the great opportunity to map the non-linear stages 
of the universe evolution starting from a much better understanding 
of its primordial phase and properties.
The geometry and topology of the universe could be 
also probed by the {\sc Planck} capability to accurately 
measure the low multipole region with an excellent control
of the Galactic foregrounds.
The wide multipole range covered by {\sc Planck}  
will help the comprehension of reionization 
(and the discrimination among several reionization scenarios) 
and the determination of the power spectrum of primordial perturbations.
Last, but not least, {\sc Planck}
will allow to properly understand the interplay 
between these different aspects. 

Although the observational difficulties and in spite of some 
false past detections of distortions,
the CMB spectrum represents a powerful and quite general way to probe
astrophysical and cosmological scenarios through their imprints 
associated to the energy exchanges and/or photon injections in the plasma.
Up to now, this role relies only on upper limit 
analyses mainly based on the COBE/FIRAS measures of about ten years ago.
On the other hand, while a CMB spectrum close to a blackbody is a necessary 
requirement of the current cosmological model, 
many physical processes in all the current cosmological 
and astrophysical scenarios predict the existence of small distortions.
Their detection represents a crucial probe for current cosmology
and their accurate measure would provide a relevant information
complementary to that contained in the CMB anisotropy pattern.
On the contrary, the possible lack of their detection
would represent a problem for our
understanding of the evolution of the universe
as it would have been 
if the anisotropies were missed by COBE/DMR.

The space is again the favourite or, more realistically, the necessary 
laboratory to reveal the CMB spectral distortions.
Late distortions and in particular Comptonization distortions
with $\Delta \epsilon / \epsilon_i \approx 10^{-6}-10^{-5}$
are predicted in quite well established 
astrophysical contexts 
and some classes of less conventional cosmological processes
might also have injected similar fractional energy amounts 
at early epochs (or much larger for $z_h \rightarrow z_{therm}$).
The examples focussed in this review 
strongly support the existence of late distortions on the basis of the 
current WMAP evidence of a reionization at substantial redshifts. 
Note that, except for cooling processes
(that are probably quite unrealistic in the light
of the WMAP results), 
the contributions from different processes 
to late spectral distortions are additive.
As discussed in Sect.~\ref{sec:spec_dist}, 
experiments like DIMES and FIRAS~II, 
considered here as reference proposals,
have the sensitivity and frequency coverage necessary to detect 
both late and early distortions, 
to accurately measure the corresponding parameters, 
and to clearly discriminate between them 
on the basis of the different imprints, more or less remarkable, 
that they could have left at different wavelengths.
Therefore, the realization of such very accurate 
CMB spectrum experiments will represent a fundamental 
experimental challenge of the future space cosmology. 



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\end{thebibliography}