The CMB Initial Data and Fundamental Operator Quantization of General Relativity
Victor N. Pervushin
Bogoliubov Laboratory of Theoretical Physics
141980 Dubna
Russia
The observational data on CMB radiation revealed that our Universe can be an ordinary physical object moving with respect to the Earth observer with the occasional initial data. This fact allows us to apply the theory of irreducible unitary representations of the Poincare group in order to describe the Universe in the framework of the fundamental operator quantization of General Relatvity and Standard Model of elementary particles. The simplest fit of the observational CMB data is given that includes occasional gauge-invariant and frame-covariant initial data and their units of measurement.
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\title{The CMB  Initial
Data  and
 Fundamental Operator Quantization
 of General Relativity}

\author{Victor N. Pervushin,\\
Bogoliubov Laboratory of Theoretical Physics,\\
Joint Institute for Nuclear Research, 141980 Dubna, Russia}

\begin{document}

\maketitle



\begin{abstract}

The observational  data on CMB radiation revealed that our
Universe can be an ordinary physical object moving with respect to
the Earth observer with the occasional initial data. This fact
allows us to apply the theory of irreducible
  unitary representations of the Poincare group in order to
  describe the Universe
   in the framework of the fundamental operator
quantization of General Relatvity and  Standard Model
  of  elementary particles.
 The simplest fit of the observational
CMB data is given that includes occasional gauge-invariant and
frame-covariant initial data and their units of measurement.






\end{abstract}



\vspace{4cm}

\hfil submitted to

\vspace{.51cm}

\hfil {\small XXXIII INTERNATIONAL CONFERENCE ON HIGH ENERGY
PHYSICS}



 \hfil {\small Particle astrophysics \&
cosmology }

\vspace{1cm}

 \hfil {\small ICHEP'06 Moscow, 26.07- 02.08, 2006}

 \hfil  {http://ichep06.jinr.ru}



 \vspace{1cm}

%
\newpage

\tableofcontents



\section*{Introduction}

  The measurements of the
 Cosmic Microwave Background (CMB) radiation
  temperature  \cite{WMAP} revealed
   the comoving frame of the Universe
   distinguished by its dipole component measured in the rest frame
 of an Earth observer, i.e. his ``Hubble''
  Telescope. We
 believe that the velocity and
 and initial position are occasional values that have no relation
 to the equations of motion and their fundamental parameters of
 the type of the Planck mass.  One can say that the occasional
 motion of the CMB
  comoving frame with respect to the rest frame
  of an observer returned back  us to the historical
 pathway of physics, where occasional  initial data
  are considered as  ingredients supplementing equations of motion
 of any physical theory including the General
 Relativity (GR) \cite{Y,pvng8a,pvng8b}.
  The  occasional  initial data  should not depend on
   the equations of motion (i.e., laws of
 nature) including their fundamental parameters  of
 the type of the Planck mass formed by the Newton coupling constant in GR.


 This historical tradition to separate any theory
 into two independent parts ``equations'' and ``data''
  gives us another admissible alternative
   to the main supposition of the
 Inflationary Model \cite{linde}, according to which the initial data
 of the Universe evolution in GR are
 defined by the  Planck mass as one of the fundamental parameters
 of the equations of motion.


  In  contrast to the  Inflationary Model, the revelation
  of the comoving frame of our Universe allows us to seek
  explanations of  cosmological problems, or part of them,
   with the help of the ordinary Laplace-type questions:
  What are  primordial values
  of the cosmological scale factor (that can be considered here as
  a  gauge-invariant evolution
  parameter \cite{pvng8b}) and its velocity? What are the units of measurement of the
  gauge-invariant and relativistic covariant initial data
  which can give us the simplest fit of all observational data?



 The description of the Universe
  in its comoving frame of reference
   allows us to apply for the construction of gauge-invariant
   variables the theory of irreducible
  unitary representations of the Poincare group and
  {\it fundamental operator quantization} of  GR and Standard Model (SM)
  of  elementary particles
  developed  by Dirac, Heisenberg,
 Pauli, and Schwinger in the case of QED (see \cite{Dir,sch2,pol}).
 A question arises: What does
 {\it fundamental operator quantization} mean
  for both  the SM and GR?
 The answers to all these questions are the topics of the paper.
 We shall list here numerous results on
  the fundamental quantization of GR obtained by the founders
  of  modern theoretical physics and
 give a set of theoretical and observational arguments
 in favor of that this quantization of GR and SM can
 describe the creation of the Universe from
 vacuum in the frame of reference associated with
  the CMB radiation.

\section{Fundamental Operator Quantization}

\subsection{Fundamental Operator Quantization of Electrodynamics and Initial Data}

 Now the point of view is  generally accepted that
 physical results in any gauge theory
 should not depend on any ``frame of reference''.
  This point of view is based on the Faddeev -- Popov heuristic
      quantization \cite{fp1}
      in the frame free Lorentz gauge, as these results
      do not depend on ``gauge''.

      What is wrong in this assertion? Wrong is  slang:
      ``frame of reference''. The right complete phrase is
      ``frame of reference   to initial data'';
    therefore,  physical results as solutions
    of the equations of motion depend on the initial data, given in
    a concrete  frame, and
    the very equations of motion do not depend on the frame, i.e initial
    data, as Galilei defined frame transformations as the ones of
    initial data. The relativistic transformations are only
    the generalization of the Galilei ones.
  Therefore, the problem of initial data
  in any relativistic field theory could  be solved in
  the  comoving frame distinguished by the
  unit  time-like vector ($l^{(0)}_\mu=(1,0,0,0)$).


  In particular, in electrodynamics, this unit  time-like vector
  separates  vector field components $A_\mu$ into time-like $A_0$ and
  the space-like ones $A_j$. The latter are split,
 in agreement with the theory of
 irreducible representation of the Poincare group \cite{ss},
  on two transverse degrees of  freedom $A^{(\rm T)}_i=
  (\delta_{ij}-\partial_i\frac{1}{\triangle}\partial_j)A_j$
  with gauge-invariant initial data (called the ``photon'')
   and the longitudinal part $A^{(||)}_i=
   \partial_i\frac{1}{\triangle}\partial_jA_j$
   which together with the time-like component $A_0$ form
   the gauge-invariant Coulomb  potential $A_0^{(\rm
   T)}=A_0-\partial_0\frac{1}{\triangle}\partial_jA_j
   $ without initial data.  Dirac \cite{Dir} called this gauge-invariant
   functionals $A^{(\rm T)}_\mu,\Psi^{(\rm T)}
   =\exp\{ie\frac{1}{\triangle}\partial_jA_j\}\Psi$ the ``dressed'' fields.
    The propagator of the ``dressed'' vector field
    \cite{Dir,pol}\footnote{The similar relativistic-covariant construction for a massive
    vector field propagator was given in \cite{pvn6}
    \begin{equation}\nonumber
\label{sm} D^R_{\mu\nu}(q) = \delta_{\mu 0}\delta_{\nu 0}{1\over
({q_k}^2+M^2)} +\delta_{\mu i}\delta_{\nu j}
\left(\delta_{ij}-{q_iq_j\over ({q_k}^2+M^2)}\right){1\over
q_0^2-q_k^2-M^2-i\varepsilon}.
\end{equation} }
 \begin{equation}
\label{qed} D^R_{\mu\nu}(q) = \delta_{\mu 0}\delta_{\nu 0}{1\over
{q_k}^2} +\delta_{\mu i}\delta_{\nu j}
\left(\delta_{ij}-{q_iq_j\over {q_k}^2}\right){1\over
q_0^2-q_k^2-i\varepsilon}~.
\end{equation}
  contains the instantaneous Coulomb
 interaction that forms instantaneous atoms and molecules.
 Nobody proved that
   these bound states  formed by the
  Coulomb  potential
  can be obtained by the  Faddeev-Popov heuristic
  quantization  \cite{fp1} in the frame free ``Lorentz gauge
 formulation'' (where all field components are considered
  as ``degrees of freedom'' on equal footing
  and all photon propagators have only the light cone singularities).
 In fact, Faddeev \cite{f1} proved the
 equivalence of this frame free gauge formulation with the Dirac
 {\it fundamental operator quantization} (\ref{qed}) \cite{Dir,pol}
  only for the scattering amplitudes of elementary particles \cite{pvn4,pvn3}.

 To his
   great surprise, a contemporary theoretician may
  know that  Schwinger
 ``{\it  rejected all Lorentz gauge formulations
as unsuited to the role of providing the fundamental operator
quantization}'' \cite{sch2}.


In the context of a consistent description of
   bound states and collective evolution
 of the type of cosmological expansion,
 one can ask what  ``{\it  the fundamental operator
quantization}'' of GR is?

\subsection{GR in the Comoving Frame of Reference}

 Einstein \cite{einsh}
proposed  GR \be\label{gr} S_{\large \rm GR}[\vh_0|F]=\int
d^4x\sqrt{-g}\left[-\dfrac{\vh_0^2}{6}R(g)
 +{\cal L}_{(\rm M)}\right],
 \ee
where $\vh_0=M_{\rm
 Planck}\sqrt{3/{8\pi}}$ is the Planck
mass parameter, as
 generalization of the Lorentz frame group, whereas Hilbert  \cite{H}
 formulated GR so that Einstein's
 generalization $x^\mu\to \widetilde{x}^\mu
 =\widetilde{x}^\mu(x^\mu)$ became a gauge group.
 Recall the principal difference between
 the frame transformations and the gauge ones.
 Parameters of  frame transformations are treated as measurable quantities
 of type of initial data,
  whereas parameters of the gauge  transformations
 (i.e., diffeomorphisms) are not measured.  Diffeomorphisms
  mean that a part of variables are converted into
   potentials without initial data due to  constraints \cite{Noter}.
 All observable initial data should be gauge-invariant.

 The separation of the frame  transformations (here the Lorentz ones)
 from the gauge transformations (here the general coordinate ones)
 can be fulfilled by using  the gauge-invariant components
  of Fock's symplex $\omega_{(\alpha)}$ defined as
$$
 ds^2=g_{\mu\nu}dx^\mu dx^\nu=\omega_{(0)}\omega_{(0)}-
 \omega_{(b)}\omega_{(b)};~~~~~~~\omega_{(\alpha)}=e_{(\alpha)\nu} dx^\nu
 $$
 where
 $e_{(\alpha)\nu}$ are
 the Fock tetrad the components of which   are marked by
 the
 general coordinate index without a bracket and
 the Lorentz index in  brackets $(\alpha)$ \cite{fock29}.

 The choice of   the time axis $l_{(\mu)}=(1,0,0,0)$ as the
 CMB comoving frame allows us to construct
 an irreducible representation of the Poincare group by
  decomposition of Fock's  vector simplex field $\omega_{(\alpha)}$
  in accordance with the  definition of the Dirac Hamiltonian
  approach to GR \cite{dir}
  \be\label{om}
  \omega_{(0)}=\psi^6N_{\rm d}dx^0\equiv \psi^2\omega^{(L)}_{(0)},~~~
  \omega_{(b)}=\psi^2 {\bf e}_{(b)i}(dx^i+N^i dx^0)\equiv\psi^2
  \omega^{(L)}_{(b)},
  \ee
 where $N^i$ is shift vector,
 $N_{\rm d}$ ~~~is Dirac's lapse function, $\psi$ is the spatial metric
 determinant, ${\bf e}_{(b)j}$ is a triad with
 the unit determinant $|{\bf e}|=1$,
 and $\omega^{(L)}_{(0)},\omega^{(L)}_{(b)}$ are
 the scale-invariant Lichnerowicz simplex \cite{Y}
 forming the scale-invariant volume
 $
 dV_0 \equiv
 \omega^{(L)}_{(1)}\wedge \omega^{(L)}_{(2)}\wedge\omega^{(L)}_{(3)}=d^3x
 $
 that coincides with the spatial coordinate volume.
  This classification allowed
  Dirac to separate  all components with zero canonical momentum
 ($N_{\rm d},N_{(b)}=N^j{\bf e}_{(b)j}$) in the GR action   as the potentials
 (i.e. variables without the initial data)
  obtained by the resolution of
 the energy constraint
 \be\label{1ec}
 \frac{\delta S}{\delta N_{\rm d}}\equiv -T_0^0=0
 \ee and momentum one
   \be\label{1mc}
   \frac{\delta S}{\delta N_j}\equiv -T_0^j=0.
   \ee
 Equations
\bea\label{1pc}
 \frac{\delta S}{\delta \log \psi}&\equiv & -T_{\psi}=0,\\
 \label{1ee}
 \frac{\delta S}{\delta {\bf e}_{(b)j}}&\equiv & -T_{(b)}^j=0
 \eea
 can be considered as the dynamic ones.

   \subsection{Gauge-Invariant Variables and Spatial Coordinates}

 %The gauge-invariant
% variables  as stated above
% mean here nothing but the application of the standard theory
% of the unitary irreducible representations of the Poincare group.
 It is well known \cite{Y} that the construction of
 tensor and vector variables invariant with respect to
 the general spatial coordinate transformations $x^j \to
 \widetilde{x}^j=\widetilde{x}^j(x^0,x^j)$ repeats the Dirac construction of
 QED with the one-to-one
 correspondence $[ A^{(\rm T)}_0,A^{(\rm T)}_k]~\to~[N^{(\rm T)}_{(b)},
 e^{(\rm T)}_{(b)k}]$.
  Eqs. (\ref{1ee}) describe only
   two transversal gravitons distinguished by the constraint
 \be\label{c1}
\partial_i{\bf e}^{(\rm T)i}_{(b)}\simeq 0,
 \ee
 and constraint (\ref{1mc})  determines only
 two  potentials from three $N^{j}$ (whereas
 the scalar potential $\partial_j [\psi^6N^j]$ can be arbitrary)
 \cite{Y,pvng8a}.
 This means that the  spatial coordinates
 and the Lichnerowicz volume $V_0=\int d^3x$ can be identified
 with  observable in accordance with the Dirac definition \cite{Dir}.

\subsection{Cosmological Scale Factor as a Gauge-Invariant Evolution Parameter}

  In contrast to tensor and vector components,
  the scalar sector $N_{\rm d},\psi,\partial_j [\psi^6N^j]$ in GR
   goes out from the analogy with QED. The problem is the invariance
  of  GR action in the comoving frame
   with respect to the reparametrizations of the
 coordinate evolution parameter: $x^0 \to
 \widetilde{x}^0=\widetilde{x}^0(x^0)$ \cite{6}. This means that
 the coordinate evolution parameter $x^0$ is not
 observable. Therefore, the role of a time-like variable is played by
   one of the dynamic variables.
  A similar situation  is in Special Relativity
 (SR), where  the role of a timelike variable is played by
   one of the dynamic
 variables  $X_0$ in the World space of events $[X_0|X_k]$.
 The reparametrization invariance  leads to the energy constraint
 the
 solution of which with respect to the canonical momentum
 of the timelike variable is identified with the energy
 of the relativistic particle. Recall that the primary and secondary
  quantizations of the energy constraint give   the
   quantum field theory of particle creation as a physical consequence
   of the unitary irreducible representation of the Poincare group.


 Wheeler and DeWitt \cite{WDW1,WDW2} proposed considering the
 reparametrization invariance
 in GR in a similar manner, i.e. they proposed to generalize
 the construction of the unitary irreducible representation
 of the Poincare group in the Minkowskian space of events $[X^0|X^i]$
 to the field space of events in GR. In the case of the  finite space considered in the modern
 cosmology for description of the Universe, the role of
 reparametrization-invariant evolution parameter
   (i.e. a time-like variable in the field space of events) is
   played by
  a  cosmological scale factor $a(x^0)$. This factor is
  separated by the scale transformation of all fields with a conformal
  weight $n$ including
 the metric components
 $$
 F=a^n(x^0) \widetilde{F}^{(n)},~~~~~~
 g_{\mu\nu}=a^2(x^0)\widetilde{g}_{\mu\nu}
 $$
 This transformation keeps the momentum constraint
 $T^k_0=\widetilde{T}^k_0=0$, so that
 the cosmological scale factor $a(x^0)$ can be
 considered as the zero mode solution
 of the momentum constraint \cite{pvn7}.

 The separation of the cosmological scale factor is well-known
 as the ``cosmological perturbation theory''
 (where $\widetilde{\psi}=1-\Psi/2,\widetilde{\psi}^6\widetilde{N}_{\rm d}=1+\Phi$)
  proposed by Lifshits
 \cite{lif} in 1946 and applied now for analysis of
 observational data in modern astrophysics and cosmology
  (see  \cite{bard}). It is generally accepted \cite{lif,bard} that
 the cosmological scale factor is an additional variable without
 any constraint for the deviation $\Psi$, so that
 $\int d^3x \Psi\not = 0$, and there are two zero Fourier harmonics
 of the determinant logarithm
 instead of one. This doubling
 in the ``cosmological perturbation theory''  \cite{bard}
 does not allow to express the velocities of
 both variables $\log a$ and $\int d^3x \Psi$ through
 their momenta and to construct the Hamiltonian approach to GR
 \cite{pvng8a,pvng8b}. In order to restore GR, the logarithm of
 the cosmological scale factor is identified with the Lichnerowicz spatial
 averaging of the  spatial determinant logarithm
 \be\label{csf}
  \log a = \langle \log \psi^2\rangle\equiv \frac{1}{V_0}\int d^3x\log
  \psi^2.
 \ee
 The local part of the spatial determinant logarithm
 $\log\widetilde{\psi}^2\equiv\log \psi^2-\langle \log \psi^2\rangle$
 satisfies the equality
 \be\label{lsf}
 \frac{\delta S}{\delta \log \widetilde{\psi}}\equiv
 -T_{\psi}+\langle T_{\psi}\rangle=0,~~~~~~~~
  \int d^3x\log\widetilde{\psi}^2\equiv 0.
 \ee
 This theory was called in  \cite{pvng8b}
 the ``Hamiltonian cosmological perturbation
 theory''.

 A scale transformation of a curvature
 $
 \sqrt{-g}R(g)=a^2\sqrt{-\widetilde{g}}R(\widetilde{g})-6a
 \partial_0\left[{\partial_0a}\sqrt{-\widetilde{g}}~\widetilde{g}^{00}\right]$
   converts action (\ref{gr}) into
 \be\label{1gr}
 S=\widetilde{S}-
 \int\limits_{V_0} dx^0 (\partial_0\vh)^2\int {d^3x}{\widetilde{N}_{\rm d}}^{-1},
 \ee
 where $\widetilde{S}$
  is the action (\ref{gr})  in
 terms of metrics $\widetilde{g}$ and
 the running scale  of all masses
 $\vh(x^0)=\vh_0a(x^0)$. The variation of this action with respect
 to the new lapse function leads to a new energy constraint
 \be\label{nph}
  T^0_0=\widetilde{T}^0_0-
  \dfrac{(\partial_0\vh)^2}{\widetilde{N}_{\rm d}^2}=0
  ~~~~~~~~
  \left(\widetilde{T}^0_0=-
  \frac{\delta \widetilde{S}}{\delta \widetilde{N}_{\rm d}}\right).
 \ee
 The spatial averaging of the square root
 $\sqrt{\widetilde{T}^0_0}=\pm\dfrac{(\partial_0\vh)}{\widetilde{N}_{\rm d}}$
 over the Lichnerowicz volume $V_0=\int d^3x$
 gives  the Hubble-like relation
 \be\label{Lint}
 \zeta_{(\pm)}=\int dx^0\langle \widetilde{N}_{\rm d}^{-1}\rangle^{-1}=
  \pm\int^{\vh_0}_{\vh}
  d\vh/\langle{(\widetilde{T}_0^0})^{1/2}\rangle,
  \ee
   where
  $\langle F\rangle=V_0^{-1}\int d^3x F$
  and  $d\zeta=\langle(\widetilde{N}_{\rm d})^{-1}\rangle^{-1}dx^0$ is a
time-interval invariant with respect to
  time-coordinate transformations
  $x^0 \to \widetilde{x}^0=\widetilde{x}^0(x^0)$.
  We see that the  Hubble law in the exact
 GR  appears as  spatial averaging of the energy constraint (\ref{nph}).
 Thus, in the contrast to with the generally accepted Lifshits
 theory \cite{lif} its Hamiltonian version \cite{pvng8b} distinguishes
 the variant time-coordinate $x^0$ as an object of reparametrizations
 from the reparametrization-invariant  time interval
 (\ref{Lint})\footnote{Just this interval can be identified
 in GR with the  spatial averaging of
 the conformal time of observable photons as we shall see below.}.



 Just this distinction converts
 the local part of the energy constraint (\ref{nph})
 into equation determining unambiguously
 the gauge-invariant
  Dirac lapse function
 \be\label{13ec}
 N_{\rm inv}={\langle(\widetilde{N}_{\rm d})^{-1} \rangle
 \widetilde{N}_{\rm d}}=
 {{\langle{(\widetilde{T}_0^0})^{1/2}\rangle}}
 (\widetilde{T}_0^0)^{-1/2}.
 \ee

The explicit dependence of $\widetilde{T}_0^0$ on
$\widetilde{\psi}$
  can be given in terms of the scale-invariant  Lichnerowicz
  variables  \cite{Y}
  $\omega^{(L)}_{(\mu)}=\widetilde{\psi}^{-2}\omega_{(\mu)},
  F^{(Ln)}=\widetilde{\psi}^{-n}\widetilde{F}^{(n)}$
 \be\label{t00}
 \widetilde{T}^0_0= \widetilde{\psi}^{7}\hat \triangle \widetilde{\psi}+
  \sum_I \widetilde{\psi}^Ia^{I/2-2}\tau_I, \ee
   where $\hat \triangle
 \widetilde{\psi}\equiv({4\varphi^2}/{3})\partial_{(b)}\partial_{(b)}\widetilde{\psi} $ is
 the Laplace operator and
  $\tau_I$ is partial energy density
  marked by the index $I$ running a set of values
   $I=0$ (stiff), 4 (radiation), 6 (mass), 8 (curvature), 12
   ($\Lambda$-term)
in accordance with a type of matter field contributions, and $a$
is the scale factor \cite{pvng8a}.

 The expression
 $(\widetilde{T}_0^0)^{1/2}$ is Hermitian
 if  a negative
 contribution of  the local determinant momentum
 \bea
\label{gauge}
 p_{\widetilde{\psi}}&=&\frac{\partial {\cal L}}{\partial (\partial_0\log\widetilde{\psi})}\equiv
 -\frac{4\vh^2}{3}\cdot\frac{\partial_l(\widetilde{\psi}^{6}N^l)-
 \partial_0(\widetilde{\psi}^{6})}{\widetilde{\psi}^{6}\widetilde{N_{\rm d}}},
 \eea
is removed  from the energy density (\ref{nph}) by the minimal
surface constraint \cite{Dir}
 \be\label{hg} {p_{\widetilde{\psi}}}\simeq 0 ~~~~\Rightarrow ~~~~
\partial_j(\widetilde{\psi}^6{\cal N}^j)=(\widetilde{\psi}^6)'
~~~~~ ({\cal N}^j=N^j\langle \widetilde{N}_{\rm d}^{-1}\rangle).
 \ee
One can see that the scalar sector $N_{\rm
int},\widetilde{\psi},\partial_j [\widetilde{\psi}^6{\cal N}^j]$
is completely determined in terms of gauge-invariant quantities by
the equations (\ref{lsf}), (\ref{13ec}) and (\ref{hg}), where
${T}_{{\psi}}$ in Eq. (\ref{lsf}) is given as \be\label{tp}
 {T}_{{\psi}}|_{(p_{\widetilde{\psi}}=0)}=7N_{\rm inv}
 \widetilde{\psi}^{7}\hat \triangle \widetilde{\psi}+
  \widetilde{\psi}\hat \triangle[N_{\rm inv}\widetilde{\psi}^{7}]+
  \sum_I I\widetilde{\psi}^Ia^{I/2-2}\tau_I. \ee

These equations are in agreement with the Schwarzschild-type
solution for the potentials
$\triangle\widetilde{\psi}=0,\triangle[N_{\rm
inv}\widetilde{\psi}^{7}]=0$ in the empty space $\tau_I=0$, but
they strongly differ
  from the ``gauge-invariant'' version
\cite{bard} of the Lifshits perturbation
 theory   \cite{lif}.

 First of all, the Lifshits theory \cite{bard}
 considering the scale factor as an additional variable contains
 double counting of the homogeneous variable that is an obstruction to the
 Hamiltonian method and quantization.

 Second, the Lifshits theory \cite{bard} confuses
  the variant time-coordinate with the
 gauge-invariant observable ``conformal time''
 of a cosmic photon. This confusing loses the relativistic
 treatment of the scale factor $\vh$ as the evolution parameter
  in the field space of events
 $[\vh|F^{(L)}]$, where
 its canonic momentum is
  the energy  as the solution of the energy
 constraint. In other words, the Lifshits theory \cite{bard}
 loses the standard Hamiltonian solution of
 the problem of the initial data for the scale factor
 $\vh$  \cite{pvng8a}.

 Third, the Lifshits theory \cite{bard}
 does not take into account
  both the Dirac  constraint (\ref{hg}) removing
  the negative energy of the spatial determinant and
   the potential scalar perturbations formed by the
    determinant
   $\widetilde{\psi}=1+(\mu-\langle\mu\rangle) $ in (\ref{t00}), where
$\sum_I \widetilde{\psi}^Ia^{I/2-2}\tau_I=\sum_n
c_n(\mu-\langle\mu\rangle)^n\tau_{(n)}$,
 $\tau_{(n)}
 \equiv\sum_II^na^{\frac{I}{2}-2}\tau_{I}\equiv \langle\tau_{(n)}\rangle +
 \overline{\tau}_{(n)}$, and
 $\overline{\tau}_{(n)}={\tau}_{(n)}-\langle\tau_{(n)}\rangle$.
 The Hamiltonian cosmological perturbation theory \cite{pvng8a} leads
 to the scalar potentials
\bea\label{12-17}
 \widetilde{\psi}&=&1+\frac{1}{2}\int d^3y\left[D_{(+)}(x,y)
\overline{T}_{(+)}^{(\psi)}(y)+
 D_{(-)}(x,y) \overline{T}^{(\psi)}_{(-)}(y)\right],\\\label{12-18}
 N_{\rm inv}\widetilde{\psi}^7&=&1-\frac{1}{2}\int d^3y\left[D_{(+)}(x,y)
\overline{T}^{(N)}_{(+)}(y)+
 D_{(-)}(x,y) \overline{T}^{(N)}_{(-)}(y)\right],
  \eea
 where $ \beta=\sqrt{1+[\langle \tau_{(2)}\rangle-14\langle
 \tau_{(1)}\rangle]/(98\langle \tau_{(0)}\rangle)}$,
 \be\label{1cur1}\overline{T}^{(\psi)}_{(\pm)}=\overline{\tau}_{(0)}\mp7\beta
  [7\overline{\tau}_{(0)}-\overline{\tau}_{(1)}],
 ~~~~~~~
 \overline{T}^{(N)}_{(\pm)}=[7\overline{\tau}_{(0)}-\overline{\tau}_{(1)}]
 \pm(14\beta)^{-1}\overline{\tau}_{(0)}
 \ee
 are the local currents, $D_{(\pm)}(x,y)$ are the Green functions satisfying
 the equations
 \bea\label{2-19}
 [\pm \hat m^2_{(\pm)}-\hat \triangle
 ]D_{(\pm)}(x,y)=\delta^3(x-y)-\frac{1}{V_0},
 \eea
 where $\hat m^2_{(\pm)}= 14 (\beta\pm 1)\langle \tau_{(0)}\rangle \mp
\langle \tau_{(1)}\rangle$.

  These Hamiltonian solutions (\ref{12-17}) and (\ref{12-18})
  do not contain
the Lifshits-type kinetic scalar perturbations
 explaining the CMB spectrum in the Inflationary Model
 \cite{bard}; they disappear due to the
 positive energy  constraint (\ref{hg}). Therefore, the problem arises
  to reproduce the  CMB spectrum
   by  the fundamental operator quantization.

   In contrast to the Lifshits theory,
    the solutions (\ref{12-17}) and (\ref{12-18}) contain
    the nonzero shift-vector ${\cal N}^i$ of the coordinate origin
   with the spatial metric oscillations that lead  to the new mechanism of formation
  of the large-scale structure of the Universe \cite{pvng8a,pvng8b}.



\subsection{The GR ``Energy'' and Quantum Universe}
%Thus,
% the running Planck mass $\vh(x^0)=aM_{\rm
% Planck}\sqrt{3/{8\pi}}$ scaling all masses  plays  the role
% of an evolution parameter. This means that
% the constraint value of its canonical
% momentum

%  becomes the energy of the relativistic
% Universe like the Einstein energy $E=mc^2$ in SR \cite{pvng8b}.


One can see that the spatial averaging of the energy constraint
(\ref{nph}) in terms of the scale factor canonical momentum
 \bea \label{pph}
 P_\vh&=&\frac{\partial L}{\partial (\partial_0\vh)}
 = -2V_0\partial_0\vh
 \left\langle(\widetilde{N}_d)^{-1}\right\rangle=
 -2V_0\frac{d\varphi}{d\zeta}\equiv-
2V_0 \vh',%=\pm E_\vh
 %\\
% \label{gauge}
% p_{\psi}&=&\frac{\partial {\cal L}}{\partial (\partial_0\log\widetilde{\psi})}\equiv
% -\frac{4\vh^2}{3}\cdot\frac{\partial_l(\widetilde{\psi}^{6}N^l)-
% \partial_0(\widetilde{\psi}^{6})}{\widetilde{\psi}^{6}\widetilde{N_d}},
 \eea
takes the form
  $P^2_\vh-E_\vh^2=0$, where  $E_\vh=2\int d^3x(\widetilde{T}_0^0)^{1/2}$.
 Finally, we get the field space of events $[\vh|\widetilde{F}]$,
 where $\vh$ is the evolution parameter, and its canonical momentum
 $P_{\vh}$
 plays the role of the  Einstein-type energy.

  The primary quantization of the energy
  constraint $[\hat P^2_\vh-E_\vh^2]\Psi_L=0$ leads  to
  the unique  wave function $\Psi_L$
  of the
  collective cosmic motion.
 The secondary quantization
 $\Psi_{\rm
L}=\dfrac{1}{\sqrt{2E_\vh}}[A^++A^-]$ describes   creation of a
``number'' of universes
  $<0|A^+A^-|0>=N$
  from the stable Bogoliubov vacuum  $B^-|0>=0$, where $B^-$ is
   Bogoliubov's operator of annihilation of the universe
obtained by the transformation
 $ A^+=\alpha
 B^+\!+\!\beta^*B^-$ in order to diagonalize  equations of
 motion. This causal quantization with the minimal energy
 restricts the motion of the universe in the field space of events
 $E_\vh > 0, \vh_0>\vh_I$ and $E_\vh < 0, \vh_0<\vh_I$, and it
 leads to the arrow of the time interval $\zeta \geq 0$ as the
  quantum anomaly \cite{pvng8a,gip}.


   \subsection{Hamiltonian Reduction and Problem of the Initial Data}
One can construct the  Hamiltonian form of the action (\ref{1gr})
\be\label{hf} S=\int dx^0\left[\int d^3x \left(\sum_F
P_F\!\partial_0
F\!+\!C\!-\!\widetilde{N}_d\widetilde{T}^0_0\right)\!-\!P_{\varphi}\partial_0\varphi+
\frac{P_{\varphi}^2}{4\int dx^3 ({\widetilde{N}_d})^{-1}}\right],
\ee in terms of momenta $P_{ F}=[{p_{\widetilde{\psi}}},
p^i_{{(b)}},p_f]$ and $P_\vh$ given by (\ref{gauge}) and
(\ref{pph}),
  where
 ${\cal C}=N^i {\widetilde{T}}^0_{i} +C_0p_{\widetilde{\psi}}+ C_{(b)}\partial_k{\bf
e}^k_{(b)}$
  is the sum of constraints
  with the Lagrangian multipliers $N^i,C_0,~C_{(b)}$ and the energy--momentum tensor
  components $\widetilde{T}^0_i$; these constraints include
   the transversality  $\partial_i {\bf e}^{i}_{(b)}\simeq 0$ and the Dirac
 minimal  surface \cite{dir} (\ref{hg}).

 One can find
 evolution of all field variables $F(\vh,x^i)$  with respect to
 $\vh$ by the variation of the ``reduced'' action obtained as
   values of the Hamiltonian form of the initial action  (\ref{hf}) onto
 the energy constraint  (\ref{nph}):
 \be\label{2ha2} S|_{P_\vh=\pm E_\vh} =
 \int\limits_{\vh_I}^{\vh_0}d\widetilde{\vh} \left\{\int d^3x
 \left[\sum\limits_{  F}P_{  F}\partial_\vh F
 +\bar{\cal C}\mp2\sqrt{\widetilde{T}_0^0(\widetilde{\vh})}\right]\right\},
\ee
 where $\bar{\cal C}={\cal
 C}/\partial_0\widetilde{\vh}$ and $\vh_0$ is the
 present-day datum that has no relation to the the initial
 data at the beginning $\vh=\vh_I$.
 The reduced action (\ref{2ha2}) shows us
 that the initial data at the beginning $\vh=\vh_I$ are independent of
  the  present-day ones at  $\vh=\vh_0$;
  therefore
  the proposal about the existence of the  Planck epoch $\vh=\vh_0$
   at the beginning \cite{linde} looks
  very doubtful in the framework of the Hamiltonian theory.
  Let us consider consequences of
  the classical reduced theory (\ref{2ha2}) and quantization of
  the energy constraint (\ref{nph}) without the ``Planck epoch''
  at the beginning, proposing occasional data $\vh=\vh_I,\vh'_I$ in
  agreement with the historical tradition and the Hamiltonian theory.

\section{\label{s-4}Observational Data in  Terms of Scale-Invariant Variables}



 Let us assume that the  density
 $T_0^0=\rho_{(0)}(\vh)+T_{\rm f}$
 contains a tremendous  cosmological background
$\rho_{(0)}(\vh)$.
 The  low-energy decomposition
  of ``reduced''  action (\ref{2ha2})  $2 d\vh \sqrt{\widetilde{T}_0^0}= 2d\vh
\sqrt{\rho_{(0)}+T_{\rm f}}
 =
 d\vh
 \left[2\sqrt{\rho_{(0)}}+
 T_{\rm f}/{\sqrt{\rho_{(0)}}}\right]+...$
 over
 field density $T_{\rm f}$ gives the sum
 $S|_{P_\vh=+E_\vh}=S^{(+)}_{\rm cosmic}+S^{(+)}_{\rm
 field}+\ldots$, where the first  term of this sum
 $S^{(+)}_{\rm cosmic}= +
 2V_0\int\limits_{\vh_I}^{\vh_0}\!
 d\vh\!\sqrt{\rho_{(0)}(\vh)}$ is  the reduced  cosmological
 action,
 whereas the second one is
  the standard field action of GR and SM
 \be\label{12h5} S^{(+)}_{\rm field}=
 \int\limits_{\zeta_I}^{\zeta_0} d\zeta\int d^3x
 \left[\sum\limits_{ F}P_{ F}\partial_\eta F
 +\bar{{\cal C}}-T_{\rm f} \right]
 \ee
 in the  space determined by the  interval
 $
 ds^2=d\zeta^2-\sum_a[e_{(a)i}(dx^i+{\cal N}^id\zeta)]^2;
 ~\partial_ie^i_{(a)}=0,~\partial_i{\cal N}^i=0
  $
 with  conformal time
 $d\eta=d\zeta=d\vh/\rho_{(0)}^{1/2}$ as the gauge-invariant
 and scale-invariant quantity, coordinate distance
 $r=|x|$,
 and running masses
 $m(\zeta)=a(\zeta)m_0$.
 We see that
  the  correspondence principle leads to the theory,
  where the scale-invariant conformal  variables and coordinates are
    identified  with the observable ones
    and the cosmic evolution with the evolution of masses:
  $$
\frac{E_{\rm emission}}{E_0}=\frac{m_{\rm atom}(\eta_0-r)}{m_{\rm
atom}(\eta_0)}=\frac{\vh(\eta_0-r)}{\vh_0}=a(\eta_0-r)
=\frac{1}{1+z}.%\equiv\frac{\vh(\eta_0-r)}{\vh_0}
$$
The conformal observable distance  $r$ loses the factor $a$, in
comparison with the nonconformal one $R=ar$. Therefore, in this
 case, the redshift --
  coordinate-distance relation $d\eta=d\vh/\sqrt{\rho_0(\vh)}$
  corresponds to a different
  equation
  of state than in the standard one  \cite{039,Danilo}.
    The best fit to the data  including
  cosmological SN observations \cite{SN2,SN1}
 requires a cosmological constant $\Omega_{\Lambda}=0.7$,
$\Omega_{\rm CDM}=0.3$ in the case of the Friedmann
``scale-variant quantities`` of standard cosmology, whereas for
the ``scale-invariant conformal
 quantities''
 these data are consistent with  the dominance of the stiff state
of a free scalar field $\Omega_{\rm Stiff}=0.85\pm 0.15$,
$\Omega_{\rm CDM}=0.15\pm 0.10$ \cite{039}. If $\Omega_{\rm
Stiff}=1$, we have the square root dependence of the scale factor
on conformal time $a(\eta)=\sqrt{1+2H_0(\eta-\eta_0)}$. Just this
time dependence of the scale factor on
 the measurable time (here -- conformal one) is used for a description of
 the primordial nucleosynthesis \cite{Danilo,three}.
Thus, the stiff state formed by a free scalar field
\cite{039,Danilo} can describe  in the relative (conformal) units
all epochs including the creation of a quantum universe at
$\vh(\eta=0)=\vh_I,H(\eta=0)=H_I$.

\section{Creation of Matter  and Initial Data of the Universe}
 The initial data $\vh_I,H_I$ of the universe can be  determined
 from the
 parameters of matter cosmologically created from the stable
 quantum
 vacuum  at the beginning of the universe.

 1. The Standard
 Model in the framework of the perturbation theory
 and the fundamental operator quantization of SM
  \cite{pvn6} shows us  that  W-,Z-vector bosons
 have maximal probability of the
 cosmological creation due to their mass singularity.
 The uncertainty principle $\triangle E\cdot\triangle \eta \geq 1$
  (where $\triangle E=2M_{\rm I},\triangle \eta=1/(2H_{\rm I})$)
 testifies that these bosons can be created
 from vacuum at   the moment when   their  Compton   length
 defined by the inverse mass
 $M^{-1}_{\rm I}=(a_{\rm I} M_{\rm W})^{-1}$ is close to the
 universe horizon defined in the
 stiff state as
 $H_{\rm I}^{-1}=a^2_{\rm I} (H_{0})^{-1}$.
 Equating these quantities $M_{\rm I}=H_{\rm I}$
 one can estimate the initial data of the scale factor
 $a_{\rm I}^2=(H_0/M_{\rm W})^{2/3}=10^{-29}$ and the Hubble parameter
 $H_{\rm I}=10^{29}H_0\sim 1~{\rm mm}^{-1}\sim 3 K$ \cite{pvng7,pvng8}.

% The constant
%conformal temperature
% $T_c\sim (M_I^2H_I)^{1/3}=(M_{\rm W}^2H_0)^{1/3}\sim 3 K$
% can appear due to collision and scattering processes.
% %The distribution function of creation of
%% longitudinal  components of the W-bosons  with
% CMB radiation is described as the product of decay of
%primordial  W-,Z- bosons during
% the time-life $\eta_L\sim (2/\alpha_W)^{2/3}(T_c)^{-1}$ expressed  in terms of
%the
%  Weinberg coupling constant
%  $\alpha_W=\alpha_{\rm \tiny QED}/\sin^2\theta_{\rm Weinberg}\sim
% 0.03$   \cite{pvng7,pvng8}.
% The primordial mesons before
% their decays polarize the Dirac fermion vacuum and give the
% baryon asymmetry frozen by the CP -- violation
% so that for billion photons there is only one baryon,
%  and relative contributions of the baryon matter and radiation
%  are in agreement with observational data:
% $\Omega_b \sim \alpha_W\sim
% 0.03$, and $\Omega_R\sim 10^{-5}\div 10^{-4}$~\cite{pvng8}.
% The equations of the longitudinal vector bosons
% in SM, in this case,
% describe the ``power primordial spectrum'' of the CMB radiation.

2. The collisions and scattering processes with the cross-section
 $\sigma \sim 1/M_{\rm I}^2$ can lead to conformal
 temperature $T_c$. This temperature
   can be estimated  from the condition that  the relaxation time
 is close to the life-time of the universe, i.e.,
 can be estimated from the equation in the
 kinetic theory $\eta^{-1}_{relaxation}\sim n(T_c)\times \sigma \sim H $.
 As
 the distribution functions of the longitudinal   vector bosons
 demonstrate a large contribution of relativistic momenta
 \cite{pvng8} $n(T_c)\sim T_c^3$,
 this kinetic equation  gives the temperature of
relativistic bosons $
 T_c\sim (M_{\rm I}^2H_{\rm I})^{1/3}=(M_0^2H_0)^{1/3}\sim 3 K
$ as a conserved number of cosmic evolution compatible with the SN
data \cite{039}.
 We can see that
this  value is surprisingly close to the observed temperature of
the CMB radiation
 $ T_c=T_{\rm CMB}= 2.73~{\rm K}$.
 The equations describing the longitudinal vector bosons
 in SM, in this case, are close to
 the equations that  are  used in  the
 Inflationary Model \cite{bard} for
 description of the ``power primordial spectrum'' of the CMB radiation.


 3. The primordial mesons before
 their decays polarize the Dirac fermion vacuum and give the
 baryon asymmetry frozen by the CP -- violation
 so that $n_b/n_\gamma \sim X_{CP} \sim 10^{-9}$,
 $\Omega_b \sim \alpha_{\rm \tiny QED}/\sin^2\theta_{\rm Weinberg}\sim
 0.03$, and $\Omega_R\sim 10^{-4}$~\cite{pvng8}.


 All these results
 testify to that all  visible matter can be a product of
 decays of primordial bosons, and the observational data on CMB
  reflect rather  parameters of the primordial bosons, than the
 matter at the time of recombination. In particular,
 the length of  the semi-circle on the surface of  the last emission of
photons at the life-time
  of W-bosons
  in terms of the length of an emitter
 (i.e.
 $M^{-1}_W(\eta_L)=(\alpha_W/2)^{1/3}(T_c)^{-1}$) is
 $\pi \cdot 2/\alpha_W$.
 It is close to the value of
 orbital momentum with the maximal $\Delta T$:
 $l_{(\Delta T_{\rm max})}\sim \pi \cdot 2/\alpha_W\sim  210 $,
 whereas $(\bigtriangleup T/T)$ is proportional to the inverse number of
emitters~
 $(\alpha_W)^3 \sim    10^{-5}$.


The temperature history of the expanding universe looks
 in relative units like the
 history of evolution of masses of elementary particles in the cold
 universe with the constant conformal temperature $T_c=a(\eta)T=2.73~ {\rm K}$
 of the cosmic microwave background.


 The  nonzero shift vector and
  the scalar potentials given by Eqs. (\ref{12-17}) and (\ref{12-18})
    determine
 in relative units \cite{039} the parameter
  of spatial oscillations
  $ m^2_{(-)}=\frac{6}{7}H_0^2[\Omega_{\rm R}(z+1)^2+\frac{9}{2}\Omega_{\rm
  Mass}(z+1)]$. The redshifts in the recombination
  epoch $z_r\sim 1100$ and the clustering parameter
 $
 r_{\rm clust.}={\pi}/{ m_{(-)} }\sim {\pi}/[{
 H_0\Omega_R^{1/2} (1+z_r)}] \sim 130\, {\rm Mpc}
 $
  recently
 discovered in the researches of large scale periodicity in redshift
 distribution \cite{da}
 lead to a reasonable value of the radiation-type density
  (including the relativistic baryon matter one)
  $10^{-4}<\Omega_R\sim 3\cdot 10^{-3}$ at the time of this
  epoch.

\section*{Conclusion}


The
 observational astrophysical data on CMB radiation
  revealed that our Universe can be an ordinary physical
  object moving with respect to the Earth observer
   with occasional initial data.
  This revelation returns  us back to the historical
  traditions of physics beginning with
     Ptolemaeus' rest frame, Copernicus' comoving
  one, and Galilei's frame transformations as the initial data ones,
  and finishing by
 representations of the Poincare group as the basis of
 {\it fundamental operator quantization} that
  includes occasional gauge-invariant and
  frame-covariant initial data and their units of measurement.
 In the context of the history of physics as a whole, in order
 to explain the World,
 a modern Laplace should ask for
{\it  the initial data of the gauge-invariant
 variables measured  in the
 relative units in the comoving frame of reference of this World}.

 The gauge-invariant
 variables mean here nothing but the application of the standard theory
 of the unitary irreducible representations of the Poincare group
 based on the time-like unit vector that distinguishes the
 comoving frame in the Minkowskian space-time.
 Another frame means a choice of another time-like unit vector connected with the
 first one by the Lorentz transformation that leads to the dipole
 component of the CMB temperature \cite{WMAP}.

  We
 gave here  a set of numerous arguments in favor of that
 the fundamental operator quantization
  can be a real theoretical basis
 for a   further detailed investigation of astrophysical
 observational data, including
  CMB fluctuations.% as one of the highlights of
% present-day cosmology with far-reaching implications and more
% precise observations are planned for the near future.
 %We listed the set of arguments
% that the fundamental operator quantization
% describes the creation of the Universe from nothing, and  together with
% the astrophysical observational data
% it testify that
% the primordial epoch was the electroweak one.

%\vspace{1cm}

{\bf Acknowledgements}\\
 The author is grateful to B. Barbashov, A. Zakharov, and V. Zinchuk for
 collaboration,
 and thanks  V. Kadyshevsky, A.~Efremov,
 V.~Priezzhev,   I.~Tkachev, and S. Vinitsky
 for fruitful discussions.

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\end{document}
S. Schweber, {\it An Introduction to Relativistic Quantum Field
Theory}, Row, Peterson and Co,  Evanston, Ill., Elmsford, N.Y,
1961.
\bibitem {Logunov}  N. N. Bogoliubov, A. A. Logunov, A. I. Oksak,
I. T. Todorov,
{\it Obshie Prinzipi Kvantovoj Teorii Polja}, 1st edn.,  Nauka,
Moscow, 1987.

%\bibitem{Logunov}  N.N. Bogoliubov,  A.A. Logunov,  A.I. Oksak,
%I.T. Todorov, {\it  Obchshie Prinzipy Kvantovoj Teorii Polja}, Nauka, Moscow,
%1987.
\bibitem{mo} Duff
M.J., ``The world in eleven dimensions: supergravity,
supermembranes and M-theory'', I.O.P. Publishing 1999,
http://bookmark.iop.org/bookpge.htm/book�5.
\bibitem{adm}
Arnowitt R., Deser S., and Misner C.W. ``Canonical Variables for
General Relativity'',
 {\it Phys. Rev.} {\bf 117}, 1595--1602 (1960).

\bibitem{pvn1} Pervushin V.N. ``Quantum Chromodynamics as the
 Microscopic Theory of Superfluidity'',  {\it Theor. Math. Phys.}
 {\bf 45},  1100--1111 (1981).
\bibitem{pvn2} Pervushin V.N. ``On the Vacuum in the Gauge Theories'',
{\it Riv. del Nuovo Cimento} {\bf 8},  N 10,  1--48 (1985).

%



\bibitem{pvn7} Gogilidze S., Ilieva Nevena,  Pervushin V.N. ``Dirac variables
and zero modes of Gauss constraint in finite volume two
-dimensional QED'',  {\it Int. J. Mod. Phys.} {\bf A 14},
3531--3542 (1999); Pervushin V. N.  {``Dirac Variables in Gauge
Theories''}, {\it Physics of Particles and Nuclei}  {\bf 34},
348--376 (2003);
 {\it Lecture Notes in DAAD Summerschool on  Dense Matter in
 Particle - and Astrophysics}, JINR, Dubna, Russia, August 20 - 31, 2001;
 [hep- th/ 0109218]; %\bibitem{pvn8}
 Lantsman L.D.  and  Pervushin V.N. {``Monopole Vacuum in
Non-Abelian Theories'',} {\it Physics of Atomic Nuclei}  {\bf 66},
 1384--1394 (2003).

\bibitem{pvng1}
 Gyngazov L.N., Pawlowski M., Pervushin V.N., and Smirichinski V.I.
  ``Proper Time Dynamics in General Relativity and Conformal
 Unified Theory'', {\it General Relativity and Gravitation} {\bf
 37},
 128--38 (1998).
%
%%101
\bibitem{pvng2}
 Pawlowski  M., Papoyan V. V., Pervushin V. N., Smirichinski V.I.
 ``Conformal Unification of General Relativity and Standard Model for
Strong and Electroweak Interactions'', {\it Phys.Lett.} {\bf B
418}, 263--269 (1998).



\bibitem{thw} %G. `t Hooft, Nucl. Phys. B {\bf 33}, 173 (1971); Ibid.
%{\bf 35}, 167 (1971); \\ G. `t Hooft and M. Veltman, Nucl. Phys. B
%{\bf 44}, 189 (1972); Ibid. {\bf 50}, 318 (1972).
 `t Hooft G.  and Veltman M. ``Regularization and renormalization of
gauge fields'', {\it Nucl. Phys.}, {\bf B  44}, 189-2001 (1972).


\bibitem{db}  Bardin D. and Passarino G. {``The standard model in the making:
precision study of the electroweak interactions''}, Clarendon,
Oxford, 1999.



\bibitem{ar} Manuel F.E. {``The religion of Isaac Newton''}, Oxford, 1974;\\
Westfall R.S. {``Never at rest: A biography of Isaac Newton''},
Cambridge, 1982:\\
 Koyr\'e A. {``Newtonian studies}'', L., 1965.

\bibitem{flo} Florovsky G.V. {``Orient
 fathers of the 4th
century''}, Paris, 1931; Russian translation, Moscow, 1992.
\bibitem{mey} Meyendorff John {``Byzantyne Theology.
 Trends and Doctrinal Themes''},
Fordham University Press, N.Y., 1979.

\bibitem{god1}  G\"odel K. ``Uber formal unentscheidbare Satze der
Principia Mathematica und verwandter Systeme I'', {\it Monatshefte
fur Math. und Phys.} {\bf 38}, 173--198 (1931);(Reprinted and
translated in Godel, Kurt, 1986, Collected Works, {\bf 1},
144--195, Oxford: Oxford University Press).

%\bibitem{god2}   G\"odel K. {\it Monatshefte fur Math. und Phys.}
%{\bf 37}, 349 (1930).



%{\it Sitzungber. Preuss. Akad. Wiss.} {\bf B 44}
%  N.2,  778 (1915); ibid,  {{\bf B 48} N.2,}  844 (1915).

\bibitem{poi}
 %{Poincare H.}   {\it C.R. Acad. Sci., Paris.} {\bf 140.} 1504(1905);
 {Poincare H.} ``Sur la dynamique de l'electron'', {\it
 Rendiconti del Circolo matematico di Palermo} {\bf 21} 129 (1906).

%
%\bibitem{pvng3} Pawlowski  M. and  Pervushin V.N.
%``Reparametrization-Invariant
%Path Integral in GR and ``Big Bang" of Quantum Universe'', {\it
%Int.~J.~Mod.~Phys.} {\bf A 16},   1715--42 (2001);
%[hep-th/0006116].
%
%\bibitem{pvng3a} Barbashov B.M., Pervushin V.N., and Pawlowski M.
%``Reparametrization--invariant dynamics of  relativistic
%systems'', {\it Physics of Particle and Nuclei} {\bf 32}, 546--604
%(2001).
%
%%114
%\bibitem{pvng4} Barbashov B.M. and~Pervushin V.N.
%``Reparametrization-invariant reduction in the Hamiltonian
%description of  relativistic string'', {\it Theor. Math. Phys.}
% {127},  483--493 (2001); [hep-th/0005140].



%115
%





\bibitem{pvng6} Barbashov B.M., Pervushin V.N., and Proskurin D.V.
{``An Excursus into Modern Cosmology'',}
 {\it Physics of Particles and Nuclei} {\bf 34}, Suppl. 1,
S68--S90 (2003).


 Dirac -- Schwinger ``fundamental operator quantization'' \cite{sch2} of
 Weinberg -- Salam -- Glashow \underline{Standard Model} in the Kopernik-type
 comoving frame of the Universe, where all field components
  are separated into ``potentials'' (without initial
 data) and ``degrees of freedom'' (of initial data) with different
 poles of their propagators.

 Recall that Faddeev proved the theorem of
 equivalence of ``fundamental operator quantization'' \cite{sch2,pvn2}
  with the frame free ``Lorentz gauge
 formulation'' (where all field components are considered
  as ``degrees of freedom'' on equal footing)
  only for the scattering amplitudes. Nobody proved
  even in QED that instantaneous atoms and molecules formed by the
  Coulomb  potential
  can be obtained by the  Faddeev-Popov heuristic
  quantization \cite{fp1} in the frame free Lorentz gauge where
  all propagators have only the light cone singularities. To his
   great surprise a contemporary theoretician can
  know that  Schwinger
 ``{\it  rejected all Lorentz gauge formulations
as unsuited to the role of providing the fundamental operator
quantization}'' \cite{sch2}.
 Thereupon, it is worth  emphasizing that Schwinger following Dirac
  postulated the higher
 priority of the quantum principles in
 comparison with relativistic ones \cite{dir,Dir}\footnote{
 Modern M-theories with D=26, D=10,11 \cite{mo} are consequences of
 the ``scattering branch'' of the Faddeev -- Popov-type heuristic quantization
 \cite{fp1}.
 The fundamental operator quantization of a relativistic
 string leads to R\"ohrlich spectrum without the Virasoro algebra \cite{pvng7a}.
In any case, the SN data \cite{SN1,SN2} in relative units
compatible with
 Conformal Dark Energy  is described by a scalar field,
  so that the  scalar sector of the sum of GR and SM
 can be  the conformal
 D=6 brane in the 4th-dimensional spacetime.
}.

\section{Fundamental Operator Quantization}






 %The successful predictions of neutral currents
%  and massive vector bosons by
%    the Standard Model  (SM) of the electroweak interactions
%     and its agreement with  numerous observational data
%    gave  hope to physicists that this SM together with General
%    Relativity could describe formation of the Early Universe
%    and may be its quantum creation from physical vacuum as a
%    state with a minimal {\it energy}.

     %It is accepted that difficulties to fulfill this description
%     mainly belong to GR (problems of
%     energy and time and quantization), whereas
%     the mathematical consistence of quantum field theory for SM is recognized
%      officially.

      There is the Faddeev -- Popov heuristic
      quantization \cite{fp1} in the frame free Lorentz gauge where
  all massless propagators have only the light cone singularities \cite{db}.
  Nevertheless, nobody proved
  even in QED that instantaneous atoms and molecules formed by the
  Coulomb  potential
  can be obtained by this  Faddeev-Popov heuristic
  quantization. To his
   great surprise a contemporary theoretician can
  know that  Schwinger
 ``{\it  rejected all Lorentz gauge formulations
as unsuited to the role of providing the fundamental operator
quantization}'' \cite{sch2}.
 %Thereupon, it is worth  emphasizing that Schwinger following Dirac
% Heisenberg and Pauli \cite{Dir,hp} postulated the higher
% priority of the quantum principles in
% comparison with relativistic ones.


 In fact Faddeev proved the
 equivalence of {\it fundamental operator quantization} \cite{Dir}--\cite{pvn7}
  with the frame free ``Lorentz gauge
 formulation'' (where all field components are considered
  as ``degrees of freedom'' on equal footing)
  only for the scattering amplitudes of elementary particles.


 In the context of consistent description of
  the bound states and collective evolution
 of the type of cosmological expansion,
 one can say that the modern quantum field theory is
 the fraud against taxpayers, who
 feel their discomfort from the Coulomb static electricity, and
 they know that just this electricity forms
 atoms and molecules and their bodies, but they could not find
 the Coulomb potential in the frame free version of
 QED.







\section{Physical ``Laws'' and  ``Data'' }

 The founder of the first physical theory Isaac Newton
 gave to it some pattern of the official doctrine accepted in
 his Trinity College.
 Beginning with  Newton's mechanics all physical theories  remember
 to a some extent the Christian theory of
  a human soul being in two {\it kingdoms}\,:~ a {\it kingdom} of
{\it laws} and a {\it kingdom} of {\it wills}.

 In any physical theory, a {\it kingdom of laws} is a set of equations of
 motion obtained by varying an {\it action}.
 A {\it kingdom of wills} is associated with a set of initial data
 which
 Laplace  still required for unambiguous solutions of the Newton
 equations in order ``to explain the World without God''.


 The initial data of an object  are measured
 by a set of physical instruments
 and are given by a {\it will} of
 experimenters.
  {\it Laws} of nature do not depend on the initial
 data but  results of application of these {\it laws} can depend.
 The Newton equation of a train does not depend on the initial data, i.e. on
the {\it will} of a passenger of this train who chose  his initial
position
 and the speed of the train, but the final
result of the solution of this equation  is a consequence of both
the {\it will} of the passenger and  the {\it law} of nature.

 In contrast to mathematician Laplace, physicist Newton understood
  that in any explanation
 of the Design and Purpose in the Universe  physicists
 should take into account both the  {\it kingdoms} of {laws}
 and  {``data''} given by God in a comoving reference
 frame   where  the Universe was created.


    This comoving frame is identified by modern observers
   with the
 Cosmic Microwave Background (CMB) radiation
 distinguished by its dipole component measured \cite{WMAP} in the frame
 of an Earth observer. %Who chose this frame at the time
% of formation of CMB when an Earth observer was only
% in the Project?

 Formulations of Eistein's General
 Relativity  and quantum field theory
  in a concrete frame were
 fulfilled  by the founders of modern physics
 (for details
 see \cite{dir} -- \cite{pol})\footnote{
  I was an
eye-witnesser of
  that at the beginning of the 1970s theoreticians
 restricted
 quantum field theory
  by  describing mainly scattering
 processes that do not depend on the data together with
 their reference frames.
 This restriction allowed to formulate
 the frame free Faddeev -- Popov method \cite{fp1} that gave an essential
 simplification
 of the proof of renormalizabillity (finiteness) of the Standard Model
 marked by the Nobel Prize to t'Hooft and Veltman \cite{thw}.
 But this restriction   lost
 the historical pathway of
  reference frames  in physical theories beginning with
 Copernicus until Dirac \cite{Dir} and Schwinger \cite{sch2}.
 }. Now I present here the results of our attempts
 with my collaborators \cite{pvn7} --
 \cite{pvng8b}
 to use these formulations, in order
  to describe  the creation of the Universe
 in the framework of modern physical theory in agreement with
 observational data. %, by analogy with the
% description of a moving particle in the Newton mechanics?



\section{Action and Interval as ``Foundations of Physics''}

  The official doctrine accepted in
  Trinity College
  {\it ``In the beginning was the Word ..., and the
 Word was  God''} (John 1:1) can be  consistent with the modern physics,
 if  God can be visible due to
 His action.
 The  ``action'' of the unified theory was restored
  by  both experimentalists  and
 theoreticians  in the 19th and 20th centuries in the context
 of the field nature of matter and space-time in the form of  a sum of
  Hilbert's  action of the Einstein General Relativity \cite{H}
  and the action of
 the Weinberg - Salam - Glashow Standard Model
  of elementary particles \cite{db}
   settled in the Riemannian space-time defined by a geometric interval.
   Scientists believe in that
   equations of motion
 obtained by varying this action and supplemented by the initial data
  in the CMB  frame can  explain the
 origin of the Universe.
 %What does a ``concrete frame'' mean in the modern theories?

%``Make His paths straight.'' (Mark 1:3)

\section{A  Frame for Constrained {``Data''}}
   In General Relativity (GR)
   and quantum field theories, a comoving frame was introduced  by
  Dirac, Heisenberg and Pauli, Fermi, Schwinger, and
 other physicists until the 1960s
 on the level of the action (see \cite{dir} -- \cite{pol})
  because
 it was the most  straight path to determine the
 spectrum of the elementary and collective excitations and
 to separate equations of motion from a set of
 {\it constraints} between the initial data. %\footnote{
 %In the next years, when
% the frame dependence of the physical results were considered
% as nonessential,
% frames were established on the level of equations of motion.
 %Really, the frame-equation path does not differ
% from the ``straight'' frame-action one, if we restrict tasks of
% theoretical physics by  description of scattering processes
% of elementary particles in the framework of the standard perturbation
% theory \cite{fp1}.
%I am convinced that the ``straight'' frame-action  path leads to
%results
% that essentially differ from  the frame-equation path ones, if we describe
%  collective phenomena of the type of
% bound states \cite{pvn4,pvn7},
% the string spectrum, and
%  cosmic evolution in GR \cite{pvng7a}.}.
 These {\it constraints} of the data in all modern relativistic theories are principally
 new elements in comparison with the Newton mechanics.


 A contemporary colleague of Newton in Trinity College
  could  find that the constrained relativistic systems
 led to the official Trinity doctrine
 rejected by Isaac
 Newton\footnote{Introducing the standards
 of consistent
mathematical proof into physics in terms of clear absolute notions
 Newton was looking for the
sense of these notions in Arian theology,   trying to get out of
the Trinity College doctrine which preached relativism and
logically inconsistent trinity. One can think that for Newton as a
member of Trinity College at Cambridge University this situation
was a paradox \cite{ar}.
 }
 in his dramatic discussion with the founders of this
 doctrine\footnote{One of the
 founders of the Trinity theology Basil the Great revealed
 limits
 of the {\it consistent Aristotle's logic}
(see \cite{flo,mey}) which anticipated the famous G\"odel theorems
formulated in the 20th century for {\it formal arithmetical
systems}: ~i.  Any {\it consistent} description of a system is not
{\it
 complete},

 \hspace{1cm}ii.  Any {\it complete} description of a system is not
 {\it consistent}~\cite{god1}.

\noindent Here {\it consistent} means the absence of logical
contradictions. The theological deed of Basil the Great was the
positive constructive generalization  of the {\it consistent
Aristotle's logic}, in contrast with the negative G\"odel
theorems. Basil's generalization of {\it  Aristotle's logic}
 can be formulated as a continuation of the first
two  G\"odel theorems:

 \hspace{1cm}iii. Any {\it complete} description of a
system with logical contradictions becomes
 {\it consistent} in a new meaning, if there are simultaneously
  two (or more)
 descriptions of
 the system
connected by {\it relationships}, so that two opposite assertions
about the same system belong to two  their different {\it
descriptions}.
}.




\section{Newton's doctrine versus the ``Trinity'' one}




\subsection{Two ``descriptions'' of one relativistic object}


 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%endd
 David Hilbert's
formulation of GR\footnote{In the year of celebration of the 90th
anniversary of GR
 we can now distinguish Einstein's treatment of general coordinate
 transformations (who considered them as
   generalization of the frame transformations \cite{einsh}) from Hilbert's
   variation approach to GR \cite{H}, where the general coordinate
 transformations are considered as {\it diffeomorphisms} of the GR action
 and a {\it geometric
 interval}.
  There is
  an essential difference between the frame group
 of the Lorentz -- Poincar\'e-type  \cite{poi}
  leading to a set of
 initial data
 and the {\it diffeomorphism  group} of general coordinate transformations
  restricting these initial data by {\it constraints}. This difference
  was revealed by two  N\"other theorems  \cite{Noter}.
   The formulation
  of GR in terms of
 the Fock simplex \cite{fock29} defined as a diffeo-invariant Lorentz
 vector helps us  to separate  diffeomorphisms from transformations of
 frames of reference.} in a comoving
frame of reference can be an effective illustration of the
adequateness of the  Trinity doctrine to description of any
relativistic systems (particle, string, universe in GR).

 In order to demonstrate this adequateness, let us
 consider the problem of measurements of the life-time of
 an unstable  particle being in a relativistic train moving with velocity 200 thousands km/s.
 If a Driver  of the train measures its life-time 10 s, then  a Pointsman
 at a railway station measures 14 s (see Fig. 1).
 What is a correct life-time, 10 s or 14 s?



\begin{figure}[t]
\vspace{-1cm}
 \begin{center}
\includegraphics[width=0.6\textwidth,clip]{fig2.eps}
\caption{{\small At the top of Fig.1 a relativistic train is
depicted with an unstable particle. The life-time of this particle
is measured by two observers, by a Pointsman and a Driver.
  Each of the observers has  his time:
 Pointsman - variable $X^0$, and Driver - geometrical interval
 $\eta$ (and his wave function).
 At the bottom of the figure there is an image of
 the universe where each observer has two
 sets of measurable quantities corresponding to two observers of the particle.
 To the Pointsman there corresponds a field set of measurable quantities
 (mass $\vh$ scaled by the cosmological scale factor and density of a
 number of particles), and the Driver --
  geometrical set of measurable quantities (time interval
  $\eta$  and initial data)~\cite{pvng6,pvng7,pvng8}.
} \label{fig2}}
\end{center}
\end{figure}

Two different times of the same particle
  is contradiction, in the Newton  doctrine\footnote{
  Resolving
 the Newton equation (the acceleration
  is equal to zero) one can find
 a  trajectory of the train, i.e. the
 time dependence of the coordinate of the train $X(t)=X_I+V_It$,
 where $V_I$ is a ratio of the momentum
 $P$ and a mass $m$.
The passenger can choose another frame with other
 data, but the time of a particle in all frames will be
unique and absolute, as it was postulated by Newton in his
mechanics with the  energy $E_{\rm Newton}(P)={P^2}/(2m)$. }.


Two different times of the same particle are described
  by two different  actions given in two different frames (comoving and rest),
  in the Einstein-type intermediate  doctrine\footnote{
 Lorentz, Poinc\'are, and  Einstein saw that electrodynamics
 was consistent with mechanics, where the train had the trajectory
 $X(X_0)=X_I+\frac{P}{E(P)}X_0$,
 and the energy $E(P)=\sqrt{m^2+P^2}$.
 This energy revealed and explained nuclear energetics.
 If an observer chooses another frame, the time $X_0$ converts
 into another one mixing with the coordinate
 by the kinematic Lorentz transformation
  %justified by the symmetry of
 in accordance with the Maxwell
 electrodynamics.
 This fact of changing time is one of relativistic effects
 meaning that each frame has its own time of a particle.
}, where
 the relation between these two times is only a kinematic one, but not
  a consequence of dynamic equations of motion.


 Two different times of the same particle and their relation
 as a consequence of dynamic equations of motion
 are  described by
 one Hilbert's geometro-dynamic action given in one concrete frame,
  where there is a
 bifurcation of the classical time into
 two different times (time-variable  measured by a Pointsman
  and time-interval measured by a Driver)
 of the same object.
   Isaac Newton could know in this   bifurcation the Trinity
   doctrine, because
  these two times belong to
  two different {\it descriptions} (here the dynamic
 and the geometric) of the object by the same action in the same frame\footnote{
 In order to give  the dynamic description of the relativistic
 relations, one should consider the time $X_0$ as one of the dynamic
 variables in the World space of events $[X_0|X_1]$ on equal
 footing with spatial coordinate $X=X_1$ and introduce one more
 time as a geometric measure $\eta$ of a trajectory
 $X_0(\eta)=\frac{P_0}{m}\eta,~X_1(\eta)=X_{1I}+\frac{P_1}{m}\eta$
 of a particle
 in the World space of events $[X_0|X_1]$. These equations are supplemented by
 the energy constraint $P_0^2-E^2=0,~ E=\pm\sqrt{P_1^2+m^2}$
  as an equation of the metric
 component of the Einstein interval expressed in terms of an unmeasurable
 ``coordinate time`` as an object of ``general coordinate transformation''
  in the one-dimensional  Riemannian space.
}.


 The Hilbert geometro-dynamics of a particle leads not only to Einstein-type
 theory with the  energy  explaining nuclear processes,
 but also predicts an antiparticle with a negative energy
  known as
 a Dirac positron and
reveals the historical pathway of quantum field theory  (the main
tool  of  high energy physics in the 20th century) because the
quantum field theory is nothing, but  primary and secondary
quantizations of the energy constraint,
  in order to remove a negative energy and to make a particle stable.
 However,
 the  quantum field theory uses only a time-variable
  measured by an external observer (i.e. a Pointsman)
 being out of a particle.


\subsection{Hilbert's Geometro-Dynamics of the Universe}

 In the Universe,
 an observer is simultaneously a Driver and a Pointsman.
 To the Pointsman there corresponds a field set of measurable quantities
  (the cosmological scale factor\footnote{
  In  GR,  the cosmic evolution is extracted by
 a scale transformation
${g}_{\mu\nu}=a^2\widetilde{g}_{\mu\nu}$ well known as the
cosmological perturbation theory \cite{lif,bard}. The GR action
 in
 terms of metrics $\widetilde{g}$ depends on only
 the running Planck $\vh(\eta)=aM_{\rm
 Planck}\sqrt{3/{8\pi}}$
mass scaling   all masses.}
  considered as a {\it time-like
  variable}  and densities of matter), and the Driver --
  geometrical set of measurable quantities ({\it
  time-interval}
   and initial data).
   In this case,
 geometro-dynamic relation between the {\it time-variable} and
 {\it time-interval}\footnote{
  The metric component
     $\sqrt{-\widetilde{g}}~\widetilde{g}^{00}=(\widetilde{N}_d)^{-1}$
     gives
 the conformal time of photons flying in the conformal
 flat space-time $\zeta_{(\pm)}=\int dx^0\langle N_d^{-1}\rangle^{-1}=
  \pm\int^{\vh_0}_{\vh} d\vh/\langle{(\widetilde{T}_0^0})^{1/2}\rangle$, where
  $\langle F\rangle=V_0^{-1}\int d^3x F$ is the averaging over finite
  volume $V_0=\int d^3x$, and $\widetilde{T}_0^0$ is the energy-momentum
  tensor component.} is just the famous
   Hubble law: the further a  star, the more
 redshift of the star photons. As the cosmological scale factor is
  the {\it time-variable}, its momentum
  is  the {\it energy of the
   Universe}\,\footnote{The energy constraint takes the form
  $P^2_\vh-E_\vh^2=0$, where $P_\vh$ is the scale factor canonical momentum
 and $E_\vh=2\int d^3x(\widetilde{T}_0^0)^{1/2}$ should be treated as
 the ``frame energy'' of the Universe like $E=mc^2$ in Special Relativity.}
 in the field space of events. In such the Einstein -- Hilbert GR
  the cosmic evolution is consistent with
  primary and secondary quantizations of the energy
  constraint\footnote{The primary quantization of the energy
  constraint $[\hat P^2_\vh-E_\vh^2]\Psi_L=0$ leads  to
  the unique  wave function $\Psi_L$
  of the
  collective cosmic motion.}
   justified
  by the experience of the high energy physics the 20th century.
 These quantizations  gave the
  description of the creation of the
 Universe and its geometric time and  matter from the physical
 vacuum\footnote{ The secondary quantization
 $\Psi_{\rm
L}=[{1}/{\sqrt{2E_\vh}}][A^++A^-]$ and Bogoliubov's
transformation:
 $ A^+=\alpha
 B^+\!+\!\beta^*B^-$ diagonalizes the equations of
 motion by the condensation of ``universes'' $<0|({i}/{2})[A^+A^+-A^-A^-]|0>=R$
 and describes   creation of a  ``number'' of
 universes
  $<0|A^+A^-|0>=N$
  from the stable Bogoliubov vacuum  $B^-|0>=0$.}
  \cite{pvng6,pvng7,pvng7a,pvng8b} in
  satisfactory agreement with observational
  data, if we chose
  the relative units \cite{pvng5}.
  %It was shown   that the Early
% Universe looked like  a factory of W-,Z- bosons created from the stable
% physical vacuum




 \begin{figure}[t]
\vspace{1cm}
 \begin{center}
 \includegraphics[width=0.65\textwidth,clip]{sn.eps}
\caption{ \small The Hubble diagram~\cite{pvng5} in cases of the
absolute units of standard cosmology (SC)  and the relative ones
of conformal cosmology (CC).
 The points include  42 high-redshift Type Ia
 supernovae~\protect\cite{SN2} and the reported
 farthest supernova SN1997ff~\protect\cite{SN1}. The best
fit to these data requires the dominance of the cosmological
constant density (70\%) and 25\% of the Cold Dark Matter density,
 in the case of the Friedmann  standard
cosmology, whereas for the relative units
 these data are consistent with  the dominance of density
of a free scalar field (85\%$\pm$ 10\%) with the square root
dependence of the scale factor on conformal time (that corresponds
to the stiff state) \cite{pvng5,Danilo}. \label{fig1}}
\end{center}
\end{figure}

 \subsection{Relative Units}



The cosmic dynamics of the Universe was revealed in General
Relativity by Alexander Friedmann \cite{f22} who kept in the
Einstein interval only a cosmological scale factor and resolved
equations of motion in this case. However, the interpretation of
 this cosmic dynamics as the expansion of the universe is possible
 only in the Newton doctrine of absolute units,
  if  we propose that our standards
  belong to the kingdom of {\it laws}.



 In accordance with the Trinity doctrine \cite{flo,mey},
 a man is free to choose his
 standard himself, because
 we can cognize  only
 a ratio of things. If a measurement is one of the tools of
 cognition, the Trinity doctrine means that
  we can measure any physical quantity only in units
  of another physical quantity accepted as a
  standard\footnote{Maxwell revealed that the description of results
   of experimental measurement of  electromagnetic phenomena
   by the field theory equations
 depends on the definition of measurable quantities in the theory
  and the choice of their measurement standard.
 In the introduction
  to his {``A Treatise on Electricity and Magnetism''} Maxwell wrote:
{\it ''The most important aspect
 of any phenomenon from  mathematical
 point of view  is that of a measurable quantity.
  I shall therefore consider electrical phenomena
  chiefly with a  view to their measurement,
 describing the methods of measurement, and
 defining the  standards on
  which they depend.''}%(J.C. Maxwell)
 \cite{Maxwell}.
 }.

 Defining a measurable interval of the length as the ratio
 of a Friedmann-like interval to the standard
 one that  also  belongs to  Friedmann-like intervals, one can see
 that the measurable interval of the length is not expanding,
 as it does not depend on the  cosmological scale factor.

 Really,  the scale factor
 disappears from the relative measurable interval, but not from the
 equations of motion. The equations of motion contain the
 Friedmann  cosmological scale factor as a measure of all  masses.
 It was shown~\cite{pvng5,pvng6,pvng7,pvng8} that
the relative units give a completely different physical picture of
the evolution of the universe than the absolute units of the
standard cosmology. The spectrum of photons emitted by atoms from
distant stars billion years ago remains unchanged during the
propagation and is determined by the mass of the constituents at
the moment of emission. When this spectrum is compared with the
spectrum of similar atoms on the Earth which, at the present time,
have larger masses, then a redshift is obtained.

The temperature history of the expanding universe
 copied in the relative units looks like the
history of evolution of masses of elementary particles in the cold
universe with a constant temperature of the cosmic microwave
background. The relative observable distance  loses the
cosmological scale factor $a$, in comparison with the absolute
one. Therefore, in this
 case, the observational redshift --
  coordinate-distance relation \cite{SN2,SN1}
  corresponds to the dominance of the stiff state
of free scalar field with the square root dependence of the scale
factor on conformal time   \cite{pvng5} (see also Fig. 2). Just
this time dependence of the scale factor on
 the measurable time (here -- conformal one) is used for description of
 the primordial nucleosynthesis \cite{three}.

\subsection{Electro-Weak Epoch  versus the Planck one}
Thus, the relative units doctrine  leads to a single stiff state
for
 all epochs including the creation of a quantum universe
 at the beginning.
In terms of the relative units
 the Planck mass loses  its  status as the fundamental parameter
  of the equations of motion and  becomes the present-day
  value of
 the running mass scale in contrast with the Inflationary Model
 \cite{bard,linde}
 based on the proposal   about the existence of the  Planck epoch
   at the beginning.
 The initial data of the creation  are determined by
 parameters of matter cosmologically created from the stable
 quantum
 vacuum  at the beginning of a universe.
 In the Standard
 Model,  W-,Z-vector bosons have maximal probability of this
 cosmological creation
 due to their mass singularity at
   the moment when their  Compton
   length  is close to the
 universe horizon defined by the primordial Hubble parameter.
 Therefore, the Universe was a factory of  W-,Z-vector bosons
 at the beginning. The observational data on CMB
 reflect the   parameters  of Standard Model of elementary particles
 (see Fig. 3,4) \cite{pvng7,pvng8}\footnote{Now it is a single possibility to explain the CMB
 observations  \cite{WMAP} in the
  framework of GR and SM, as it was shown in  \cite{pvng7a,pvng8b}
 the standard cosmological perturbation theory \cite{lif,bard}
 applied for  analysis of the CMB observations \cite{WMAP}
  in the Inflationary Model \cite{linde}
  has  a different number of variables
  than the Einstein  General Relativity  \cite{einsh}.}.

\begin{figure}[t]
 \centerline{\includegraphics[width=3in]{long25-v1}}
 \caption[]{\small The surface shows the distribution function of creation of
 longitudinal ($N_Z(x)$) components of the W-bosons in units of
   the dimensionless time ($\tau= 2\eta H_I$) and
the dimensionless momentum ($x = q/M_I$) with the constant
conformal temperature
 $T_c\sim (M_I^2H_I)^{1/3}=(M_{\rm W}^2H_0)^{1/3}\sim 3 K$. These bosons created
 from vacuum at   the moment when   their  Compton   length
 defined by the inverse mass
 $M^{-1}_{\rm I}=(a_{\rm I} M_{\rm W})^{-1}$ is close to the
 universe horizon defined in the
 stiff state as
 $H_{\rm I}^{-1}=a^2_{\rm I} (H_{0})^{-1}$.
 Equating these quantities $M_{\rm I}=H_{\rm I}$
 one can estimate the initial data of the scale factor
 $a_{\rm I}^2=(H_0/M_{\rm W})^{2/3}=10^{-29}$ and the Hubble parameter
 $H_{\rm I}=10^{29}H_0\sim 1~{\rm mm}^{-1}\sim 3 K$.
 CMB radiation is described as the product of decay of
primordial  W-,Z- bosons during
 the time-life $\eta_L\sim (2/\alpha_W)^{2/3}(T_c)^{-1}$ expressed  in terms of
the
  Weinberg coupling constant $\alpha_W=\alpha_{\rm \tiny QED}/\sin^2\theta_{\rm Weinberg}\sim
 0.03$
   \cite{pvng7,pvng8}.
 The primordial mesons before
 their decays polarize the Dirac fermion vacuum and give the
 baryon asymmetry frozen by the CP -- violation
 so that for billion photons there is only one baryon,
  and relative contributions of the baryon matter and radiation
  are in agreement with observational data:
 $\Omega_b \sim \alpha_W\sim
 0.03$, and $\Omega_R\sim 10^{-5}\div 10^{-4}$~\cite{pvng8}.
The equations of the longitudinal vector bosons
 in SM, in this case,
 describe the ``power primordial spectrum'' of the CMB radiation.
} \label{fig3}
\end{figure}
\begin{figure}[]
%\figurenum{1} \epsscale{0.6} {\plotone{f1j.eps}}
 \centerline{%\rotatebox{90}
 \includegraphics[width=0.55 \textwidth,height=0.71\textwidth,angle=90]{f1j.eps}}
 \caption[]{\small The curve  shows power law of the
 temperature angular power spectrum with first peak $l\sim 210$ \cite{WMAP}.
 The parameters of CMB can reflect parameters of the SM of elementary
 particles, in particular the Weinberg coupling constant
 \cite{pvng7,pvng8,pvng8b}.}
\end{figure}


 The geometro-dynamic  formulation
 of General Relativity  \cite{dir,Dir,H,fock29} supplemented by
 the cosmological scale factor as a collective time-like variable
  in a comoving frame and ``relative'' units \cite{pvng8,pvng7a,pvng8b}
  corresponds rather  the Trinity
  doctrine than the Newton one. This
  geometro-dynamics
 allows us not only to restore the historical pathway of physical
 description of the Universe evolution
 but also to use experience of quantum field theory
formulation verified by the high energy physics experiments. We
gave here  a set of numerous arguments in favor that
 this quantum unified theory (GR \& SM \& an additional scalar field)
  can be a theoretical basis
 of  the further detailed investigation of astrophysical
 observational data including
  CMB fluctuations as one of the highlights of
 present-day cosmology with far-reaching implications and more
 precise observations are planned for the near future.


\section{Design and Purpose in the Universe}


 Thus, the papers of the founders of  modern
 physics \cite{dir,Dir,H,einsh,fock29}
  allow us to restore
 the historical pathway of description of the Universe evolution
 in the comoving frame   with the definite initial data in the unified theory
 like the description of the trajectory of a relativistic
 particle in SR after its quantum creation from  stable
 vacuum. This description reveals the trinity of times in GR:
 i) the unmeasurable  coordinate time in  Hilbert's action as
 an object of general coordinate transformations (i.e., diffeomorphisms),
 ii) the diffeo-invariant geometric time-interval measured by our watch,
 and iii) the time-like variable as the cosmological scale factor
 measured by astrophysical observations and considered as a measure
 of the Universe evolution in the field space of events,
 where the Universe was created \cite{pvng1} -- \cite{pvng8b}.



 One can say that modern physics goes beyond the bounds of
 the Newton Arian doctrine accepted by modern theoreticians
 \cite{mo}
 who   have a possibility to  continue
 the Newton dialogue  with the founders of the Trinity doctrine
 \cite{flo,mey}.
 Who is a man in the Universe?
 He is a passenger who lost his rest frame in the ``frame free'' method,
 who uses only absolute units and parameters of the ''natural'' laws
 including the ``absolute Planck mass'',
 and cannot determine unambiguously the
 energy of the Universe?
 Or he is a Driver, who knows his frame and place,
  chooses his
 relative units,  measures the initial data,
 introduces new concepts and changes his
 logics as one of the tools of his cognition,  who is able to determine
 the Universe energetics, describes
  its creation, and is responsible for its further fate, as he has his
  free ``will'', in order to take part
  in further creation of the measurable world and
  to have an eternal life of his unmeasurable soul in the
 kingdom of His {will}\,?


%{\bf Acknowledgements}\\
% The author is grateful to Profs. B.~Barbashov, Z. Oziewicz,
%  and V.~Priezzhev for fruitful discussions.

%\newpage

%\noindent


\newpage

\section{Discussion at the 42nd  Karpacz Winter School of
Theoretical Physics}



 I am very grateful  to Profs. A. Borowiec and M. Francaviglia
 for the hospitality at the 42nd  Karpacz Winter School of Theoretical
 Physics on Current Mathematical Topics in Gravitation and Cosmology, L\c adek,
 Poland, 6-11.02.2006
 {\small (http://www.ift.uni.wroc.pl/karp42/)}.
 At the School there were very interesting and
 sharp debates on energy in General relativity
 (GR), its variables, and    a reference frame of the Universe
 creation.
 I list here some questions and my responses.

 \subsection*{FRAME?}

  {\bf Question by
 Prof.  Zbigniew Oziewicz} (Universidad Nacional Autonoma de M\'exico):

 What does ``the concrete reference frame of the Universe creation'' mean?
 A frame is the coordinate basis, and  physical results should not
 depend on any ``basis''.

\vspace{.31cm}

 \noindent {\bf Response (V.P.)}:

 Let me recall that the introduction of the physical concept
 of a ``reference frame'' as a three-dimensional coordinate basis with a watch
  was really stimulated
  by the great Polish astronomer  M. Kopernik who
 proposed in 1543 the heliocentric  ``frame''  as an alternative to
 the Ptolemaeus ``frame''  connected with the Earth observer.

 Thus, there
 appeared a definition of  ``physics'' as a science about observations
  (later --
 measurements) of objects being in the ``comoving frame''
  of their center of masses by devices
  associated with the ``rest frame''  of an observer.
 In the context  this definition
 Kopernik's ``relativity'' is nothing, but
 different epicycles ``relative'' to different frames.


 Galilei in his ``Dialog ...'' in 1632 converted these
 two  frames into a set of inertial frames  moving with  constant
 velocities.
  He identified one of the inertial frames with   a ship,
  where a motion of the measurable object  ``relative'' to
  a moving device is described by the difference of their
  two velocities. In this case, you are right,
  different motions of the ship do not change indications
  of the devices, i.e. initial data. I meant only motions of
  a comoving frame
  relative to a rest frame, i.e. transformations of the initial data, because
 we now have a similar situation   with
 the Cosmic Microwave Background (CMB) measured by the SkyLab
 ``Hubble'' devices being in the ``Ptolemaeus (rest) frame'' moving
 ``relative'' to CMB with the velocity 400 km/s to Leo.
 If we  move the SkyLab ``Hubble'' together with CMB
 (i.e. make the Lorentz transformations changing
  the initial data),
 the dipole components
  of CMB temperature  disappears (see \cite{pvng8a}).
 Thus, in accordance with
 Kopernik's ``relativity'' principle, the Universe as
 any ``observable'' object   has
 its ``comoving frame''  marked by CMB.


\vspace{.31cm}

\noindent {\bf Question by
 Prof.  Zbigniew Oziewicz}: %(Universidad Nacional Autonoma de M\'exico):

 What is your opinion about the relation of the Lorentz group
  to electrodynamics?


\vspace{.31cm}

 \noindent {\bf Response  (V.P.)}:

 The Faradey -- Maxwell electrodynamics contained the hidden
 symmetries revealed later by Poincare (known as the Lorentz group of
  transformations of the initial data) and
  by Weyl (known as gauge symmetry leading to constraints of initial data).
  Einstein's ``Special Relativity'' is  his generalization of mechanics
  based on the Lorentz group of frame transformations leading to
  different times ``relative'' to
   different frames and  energy $E=mc^2$ in the comoving frame.


 Einstein's ``General Relativity'' was treated by him as
 generalization of the Lorentz frame
  transformations; whereas Hilbert in his ``Foundations'' \cite{H}
  considered GR as a ``gauge'' theory with a set of constraints
  revealed by the Hilbert theorem known as the second N\"other one.
  The Lorentz transformations were introduced in GR by means of
   the Fock tetrads \cite{fock29}.


\subsection*{VARIABLES?}
 Problem of the choice of variables in different
 theories of gravitation was considered in Lectures by
 Profs. {\bf M. Francaviglia}, {\bf G. Allemandi}
 (both from  University of Torino) and
{\bf  L. Soko\l owski} (Jagiellonian University, Krak\'ow). In all
these lectures the remarkable fact
 was noted. All metric theories of gravitations are
 connected by general conformal transformations of their variables and
 they are mathematically equivalent.
 The questions appeared: What variables can be considered as
 measurable quantities? and What is the criterion of the choice
 of a true gravitation theory among the mathematically equivalent
 ones?

\vspace{.51cm}

 \noindent {\bf Response (V.P.)}

 In the context of the results presented in these Lectures
  the action of Einstein's GR is mathematically equivalent to the
  negative action of the
  conformal invariant theory of a  scalar field
  (called ``dilaton'') \cite{pvng2,pvng5}.
 The latter does not contain any dimensional fundamental
 parameter of the type of the Planck mass.
 If this action is supplemented by the SM one, where the Higgs mass is
 replaced by the ``dilaton'' field, we get the unified theory,
 where the scale (and, therefore, conformal) symmetry can be broken by the
 initial data at the beginning of the Universe provided that
 the present day value of the ``dilaton'' field is equal to the Planck mass.
 We see that the idea of conformal symmetry of the World developed
 by Richard R\c aczka (see cites in \cite{pvng2}) excludes the
 Planck epoch at the beginning of the Universe.
 Conformal symmetry distinguishes the
 Lichnerowicz {``conformal variables''}
 $g_{\mu\nu}^{(L)}=|g^{(3)}|^{-1/3}g_{\mu\nu}$
  constructed  with the help of the spatial metric determinant
  and used by Dirac in his Hamiltonian approach \cite{dir}.
  Identification of the Lichnerowicz {``conformal variables''}
  with the measurable quantities leads to Conformal Cosmology
  with varying masses (instead of the expanding Universe)
 where Supernova Data are described by the ordinary
 homogeneous free scalar field in the stiff state
 without Cosmological Constant \cite{pvng5}.


\subsection*{ENERGY?}


  The  heaviest debates at the Winter School  were
 about the choice of the energy in General Relativity
 and cosmology.
 Profs. {\bf J. Garecki} (University of Szczecin),
 {\bf L. Lusanna} (INFN, Firence),
 {\bf  L. Soko\l owski}, and {\bf M. Dyrda}
  (both from Jagiellonian University, Krak\'ow)  in their talks
   used the conventional  definition of the ADM-type energy
   relative to an external
  observer in asymptotically flat infinite spacetime.
 Profs. {\bf M. Francaviglia} (University of Torino), {\bf J.
 Lukierski} (ITF, University of Wroc\l aw) and other participants
   insisted on
 that just this
 definition could not be applied in cosmology
 because an internal observer
  has a possibility to observe only
    finite spacetime of the Universe. The  illustration
    of this discussion was  the remarkable
      film by {\bf Lorenzi Marcella} (Cosenza, Italy)
     about the Einstein energy  $E=mc^2$.

\vspace{.51cm}

 %:My talk One can suppose

%describing
% the collective motion of the observable relativistic object,

 \noindent{\bf Response  (V.P.)}

  In the Hilbert-type formulation
     of Special Relativity (SR), $E=mc^2$  is considered as a solution of
     the energy constraint  with respect to the canonical momentum
     of the time-like variable.
     Just the  GR generalization  of this SR energy $E=mc^2$
 to  the Universe in finite space
 was the topic of my talk  \cite{pvng1,pvng7a,pvng8a,pvng8b},
 where the collective time-like variable %$\vh$
 is identified with the
 homogeneous scale factor $a$
 multiplied by the Planck mass. It is a varying Planck mass
 $\vh=a M_{\rm Pl.}\sqrt{3/(8\pi)}$ considered as the
 homogeneous ``dilaton``  \underline{degree of freedom }
 in conformal version of GR.
 The Einstein-type energy in GR (as a solution of
 the energy constraint) depends on the varying mass $\vh$.
 Just  this dependence
 leads to the \underline{freedom} to
 create  the Universe and its matter from the vacuum
  in the comoving frame with the
 initial data $\vh_I^2/\vh_0^2 =a^2_I=H_0/H_I\sim 10^{-29}$ \cite{pvng7,pvng8}.






  \vspace{.51cm}

  \noindent {\bf Question by Prof.  M. Szyd\l owski} (Jagiellonian University, Krak\'ow)

  What does creation of universes from the vacuum mean?

 \vspace{.31cm}

 \noindent {\bf Response (V.P.):}

  QFT of universes is formulated  by analogy
  with  the  QFT of particles \cite{Dir} as
 the primary and the secondary quantizations of
 the  energy constraint,
 in the context of Hilbert's variational principle \cite{H}, in order to remove
 the negative Einstein-type energy
  and
 to make stable the quantum system\footnote{The existence of a stable vacuum
 as the state with minimal energy can be considered as the quantum
 analog of the Boltzmann H-theorem about the existence of
 stable temperature.}.
 We need only to understand: What does QFT mean for the ``varying masses''?
 But this problem was solved  at the end of the 60s
 for particles by Chernikov and  Parker
  with the help of  the Bogoliubov
 transformation (1946)  and
 for universes where the role of the ``mass'' is played by the
 cosmological energy density
  in 2006 \cite{pvng7a,pvng8a,pvng8b}.


 %\vspace{1cm}
\subsection*{DEGREES OF FREEDOM?}

 \vspace{.41cm}

 \noindent {\bf Question by Prof. S. Odintsov} (Barselona University \& Tomsk
 University)


  What is the status of the conformal sector of Quantum Gravity
  considered in the papers

    I. Antoniadis, E. Mottola, PRD  V. 45, 1992, p.2013;

   S.D. Odintsov, Zeit.fur Physik  V. C54, 1992, p.531;

   I. Antoniadis and S.D. Odintsov, Phys.Lett. B343, 1995, p.76 ?

 \vspace{.51cm}

 \noindent {\bf Response (V.P.):}

  These papers were devoted to GR in infinite spacetime without any
 supposition about a stable vacuum, negative energy,  initial data,
 time-variable, units~of measurement, and separation of all
 variables and metric components into degrees of \underline{freedom} with
 gauge-invariant initial data violating the frame symmetry and
 potentials without initial data, and they explained nothing.

 In particular, the kinetic energy density  of the conformal sector is
 negative. Therefore,  Dirac  (in his Hamiltonian
 approach to GR formulated in the ``comoving frame'' \cite{dir})
  identified all scalar components of the conformal sector with
 potentials.
  This identification  is in agreement with the Schwarzschild solution,
  but not with cosmological evolution that appears in the
  conformal sector,
  in the case of finite spacetime,
  as the homogeneous zero mode of the momentum constraint,
  i.e the scale factor.
  Lifshits \cite{lif} treated this cosmological scale
 factor as an additional homogeneous variable.
 However, this treatment  leads to double counting of the homogeneous variable
 and  loses a possibility
 to formulate a Hamiltonian approach
  together with quantization and the freedom
 to create the Universe from the vacuum \cite{pvng8a}.

 Dirac had no  homogeneous degree of freedom (with Hamiltonian
 and without cosmology), and Lifshits   introduced  two  (with cosmology
 and without Hamiltonian).

 In the finite volume Hamiltonian approach to GR \cite{pvng8a,pvng8b}
 the scale factor is introduced as the spatial averaging
  the spatial determinant logarithm\footnote{In this case
   the Newton potential is defined
 in the class of function with nonzero Fourier harmonics, i.e.,
 the  spatial averaging of this potential is equal to zero. This fact
  reveals a difference of the ADM-type  energy based on this potential
  from  the cosmological energy density  given in finite space
  by means of the  spatial averaging.}. The negative sign of the energy density
  of the cosmological scale factor  shows us that it is
  the evolution parameter, and the constraint value of
  its canonical momentum is the constrained energy like
  the Einstein one $E=mc^2$ in SR.
  %It is easy to convince that QFT of universe describes
%  the creation of the Universe like QFT of particles describes
%  the creation of particles.

 %The  cosmological perturbation theory \cite{lif}
% applied in the Inflationary Model \cite{bard}
% to  explain CMB spectrum   contradicts
% to the Hamiltonian approach.




\subsection*{COSMOLOGY?}
 The set of Lectures by {\bf Salvatore Capozzielo} (University of Napoli)
 was devoted to the analysis of
 ``an impressive amount of different astrophysical data''
 in the class of the $\Lambda$ - Dark Matter  cosmological models
 with the present-day
 accelerating expansion, where the nature of the $\Lambda$ dark energy
  is
 still unknown. In this class of models, all principal cosmological problems
 (homogeneity, flatness, horizon, etc)
  are solved by the inflation mechanism \cite{linde}.
 The main  test of Inflationary Model is the derivation of ``CMB primordial
 power spectrum'' \cite{bard} based on the cosmological
 perturbation theory \cite{lif}.
 There were a lot questions at the School: What is difference of the
 finite volume Hamiltonian GR   \cite{pvng8b}
 from the Inflationary
 Model  \cite{bard,linde}?

\vspace{.51cm}

 \noindent {\bf Response (V.P.)}

 The main differences between the finite volume
 Dirac Hamiltonian approach to GR  \cite{pvng8b}
 and the Inflationary Model (IM) are the following.

 1. In the finite volume GR  the observational  quantities of
 ``the cosmological scale factor''
 and the ``conformal time'' are identified with the \underline{spatial volume averaging}
  the metric scalar components, so that their
 cosmological perturbations \underline{do not contain the zero Fourier
 harmonics}, in  contrast to the Lifshits cosmological perturbation
 theory \cite{lif} used in IM \cite{bard,linde}, where
  the ``conformal time''
 is determined by the physically unattainable procedure of
 synchronization of watches in the whole Universe, and
 ``the cosmological scale factor'' is introduced as an additional
 variable that
  increases the number of variables.


 2. In the finite volume Hamiltonian GR
 the Dirac principle of  stability of
 a relativistic quantum system is used in contrast with
 IM.
 The Dirac ``stability'' means i) the zero canonical momentum fields
 are gauge-invariant potentials, ii) existence of
 the vacuum as a state with a
 minimal constrained energy, iii) the zero momentum
 of the local volume element  removing its negative energy density
 and leading to a nonzero shift-vector $N^i$ of the coordinate origin
  with
 spacial oscillations\footnote{The test of the finite
  volume Dirac Hamiltonian GR is the
 large-scale structure of the Universe (see Fig. 5).}
  and the potential scalar perturbations, whereas the
  Lifshits-type kinetic scalar perturbations
 explaining CMB spectrum in IM disappear.



3. The  CMB spectrum can be reproduced, if  the absolute units of
 length in
 IM  are replaced by the relative units  for
 which SN data are compatible with
 the state of Dark Energy as a free scalar field \cite{pvng7}.
 In this case,  the Early Universe is a factory
 of W-,Z- bosons \cite{pvng8} the equations of which reproduce
  the Lifshits-type kinetic scalar perturbations
  explaining CMB spectrum in IM. This  factory gave us all
  matter and CMB as the decay
 product of the primordial bosons created from
 the stable ``vacuum'' after the creation of the Universe
 together with its coordinate frame and  time interval known here
  as the Kopernik  comoving frame.

  In  contrast to the IM in which the cosmic evolution
  begins with
  the Planck epoch and the Planck mass is treated as
  a fundamental parameter of the ``law'', in the Hamiltonian
  GR the Planck epoch
  becomes the present-day one and the Planck mass is treated as
  the law \underline{free} datum in the comoving frame of the Universe.

\subsection*{RESUME}

 It is useful to remember that
 Newton in his Trinity College strongly distinguished the {\it kingdom of laws}
 from the {\it kingdom of \underline{freedom} (of will)}. Newton knew
 that any {\it law} does not depend on {\it will}, but application
 of the {\it law} does. The creation of the Universe is
 the application of the {\it law}. The instruction of this  application
 can present here as the historical pathway of physics:
 from empiric facts to laws and
 from {\it laws to the grace} (John 1:17) of \underline{freedom}
  to create the Universe
 from "nothing" (Newton called this  history the {\it shoulders of giants}):


%\vspace{.21cm}

 Ptolemaeus' \underline{rest frame} (RF),

 \vspace{.21cm}


 Kopernik's \underline{comoving frame} (CF),

 \vspace{.21cm}


 Galilei's  \underline{inertial frames} as a set of
 all possible \underline{initial data} given  without the law (i.e. free),

 \vspace{.21cm}


 Newton's  \underline{differential law}  invariant with respect to
 transformations of \underline{the law free initial data},

 \vspace{.21cm}


 Faraday's program: the \underline{field nature} of matter,
 and \underline{unification} of forces of Nature,

 \vspace{.21cm}


 Maxwell's  equations with hidden \underline{Lorentz's frame
 symmetry} (Poincare) and \underline{gauge} one (Weyl),

 \vspace{.21cm}


 Einstein's \underline{Special Relativity} (SR) as
 \underline{different times for different frames} (RF \& CF),

 \vspace{.21cm}

 Einstein's \underline{General Relativity} (GR)  as
 generalization of the Lorentz frame group?,

 \vspace{.21cm}

 Hilbert's \underline{variational principle} for  GR, where Einstein's
 generalization becomes gauge group,

 \vspace{.21cm}

 Fock's \underline{tetrad} as the separation of the Lorentz frame transformations from
 the  gauge ones,

 \vspace{.21cm}

 Friedmann revelation of the \underline{cosmological scale factor as
 the collective  motion} in GR,

 \vspace{.21cm}

 Einstein's $E_{\pm}=\pm mc^2$ in Hilbert's constrained
 version of SR supplemented by the \underline{interval},


 \vspace{.21cm}

 Dirac QFT for particles as \underline{the primary and secondary quantization} of the energy
 constraint,

 \vspace{.21cm}

Lichnerowicz \underline{variables}
$g_{\mu\nu}^{(L)}=|g^{(3)}|^{-1/3}g_{\mu\nu}$
 distinguished by the spatial metric determinant,

\vspace{.21cm}

  Dirac - ADM \underline{Hamiltonian approach} to GR in terms
  of radiation-type Lichnerowicz \underline{variables},

\vspace{.21cm}

 Zel'manov's global gauge symmetry of the \underline{Hamiltonian GR}
 as foundation of cosmic evolution,

\vspace{.21cm}

 Finite volume Dirac \underline{Hamiltonian approach} to  GR with
 the \underline{cosmic  motion and its energy}

\vspace{.21cm}

 $E_\vh=2\int d^3x^{(L)}\sqrt{T^{0(L)}_0}$ as the canonical  momentum
 of $\vh=a M_{\rm Pl.}\sqrt{3/(8\pi)}$ \cite{pvng8b},

\vspace{.21cm}

Hubble law in the\underline{ conformal units} as the spatial
averaging the Lichnerowicz interval,

\vspace{.21cm}

Primary and secondary quantization of the energy constraint by
\underline{Bogoliubov's transformation},

\vspace{.21cm}

 Dirac -- Schwinger ``fundamental operator quantization'' \cite{sch2} of
 Weinberg -- Salam -- Glashow \underline{Standard Model} in the Kopernik-type
 comoving frame of the Universe, where all field components
  are separated into ``potentials'' (without initial
 data) and ``degrees of freedom'' (of initial data) with different
 poles of their propagators.

 Recall that Faddeev proved the theorem of
 equivalence of ``fundamental operator quantization'' \cite{sch2,pvn2}
  with the frame free ``Lorentz gauge
 formulation'' (where all field components are considered
  as ``degrees of freedom'' on equal footing)
  only for the scattering amplitudes. Nobody proved
  even in QED that instantaneous atoms and molecules formed by the
  Coulomb  potential
  can be obtained by the  Faddeev-Popov heuristic
  quantization \cite{fp1} in the frame free Lorentz gauge where
  all propagators have only the light cone singularities. To his
   great surprise a contemporary theoretician can
  know that  Schwinger
 ``{\it  rejected all Lorentz gauge formulations
as unsuited to the role of providing the fundamental operator
quantization}'' \cite{sch2}.
 Thereupon, it is worth  emphasizing that Schwinger following Dirac
  postulated the higher
 priority of the quantum principles in
 comparison with relativistic ones \cite{dir,Dir}\footnote{
 Modern M-theories with D=26, D=10,11 \cite{mo} are consequences of
 the ``scattering branch'' of the Faddeev -- Popov-type heuristic quantization
 \cite{fp1}.
 The fundamental operator quantization of a relativistic
 string leads to R\"ohrlich spectrum without the Virasoro algebra \cite{pvng7a}.
In any case, the SN data \cite{SN1,SN2} in relative units
compatible with
 Conformal Dark Energy  is described by a scalar field,
  so that the  scalar sector of the sum of GR and SM
 can be  the conformal
 D=6 brane in the 4th-dimensional spacetime.
}.



\begin{figure}[t]
\vspace{1cm}
 \begin{center}
 \includegraphics[width=0.6\textwidth,clip]{klya.eps}
\caption{
 \label{fig5} {\small
 The diffusion of
 a system of particles moving in the space
 $ds^2=d\eta^2-(dx^i+N^id\eta)^2$ with periodic shift
 vector $N^i$ and zero momenta could be understood from an analysis
 of the following system of O.D.E.  $dx^i/d\eta=N^i$ considered for the
 two-dimensional case.
 For the system we reproduce the results of numerical
 simulations given by
    Klyatskin V.I. ~``Stochastic Equations'' M.
 Fizmatlit, 2001, where $t=\eta m_{(-)}$, $
\overline{m}_{(-)}=H_0\sqrt{{6}[\Omega_{\rm
R}(z+1)^2+({9}/{2})\Omega_{\rm
  Matter}(z+1)]/7}$} \cite{pvng8b}.
The  size $\sim 130\, {\rm Mpc}$
  of spatial oscillations of matter is in agreement
  with value of radiation-type density
  $\Omega_R\sim 3\cdot 10^{-3}$ at
  the time of diffusion $z_r\sim 1100$ \cite{pvng8b}.
  }
\end{center}
\end{figure}



% Piechocki W\l odzimierz (Warszawa, Poland)
%


\end{document}
%R\c aczka
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