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 } \leq 1.0 eV ( 95 % conf .
) , but this limit is dependent on priors .
We find that the WMAP and 2dF data alone can not 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 \leq Y _ { P } \leq 0.2471 ( 95 % conf .
) , 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 } \leq 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 .