  We have performed a thorough analysis of the constraints which can be put on
neutrino parameters from cosmological observations, most notably those from the
WMAP satellite and the 2dF galaxy survey. For this data we find an upper limit
on the sum of active neutrino mass eigenstates of \sum m_nu < 1.0 eV (95%
conf.), but this limit is dependent on priors. We find that the WMAP and 2dF
data alone cannot rule out the evidence from neutrinoless double beta decay
reported by the Heidelberg-Moscow experiment. In terms of the relativistic
energy density in neutrinos or other weakly interacting species we find, in
units of the equivalent number of neutrino species, N_nu, that N_nu =
4.0+3.0-2.1 (95% conf.). When BBN constraints are added, the bound on N_\nu is
2.6+0.4-0.3 (95% conf.), suggesting that N_nu could possibly be lower than the
standard model value of 3. This can for instance be the case in models with
very low reheating temperature and incomplete neutrino thermalization.
Conversely, if N_nu is fixed to 3 then the data from WMAP and 2dFGRS predicts
that 0.2458 < Y_P < 0.2471, which is significantly higher than the
observationally measured value. The limit on relativistic energy density
changes when a small $\nu_e$ chemical potential is present during BBN. In this
case the upper bound on N_nu from WMAP, 2dFGRS and BBN is N_nu < 6.5. Finally,
we find that a non-zero \sum m_nu can be compensated by an increase in N_nu.
One result of this is that the LSND result is not yet ruled out by cosmological
observations.
