Current cosmological bounds on neutrino masses and relativistic relics

We combine the most recent observations of large-scale structure (2dF and SDSS galaxy surveys) and cosmic microwave anisotropies (WMAP and ACBAR) to put constraints on flat cosmological models where the number of massive neutrinos and of massless relativistic relics are both left arbitrary. We discuss the impact of each data set and of various priors on our bounds. For the standard case of three thermalized neutrinos, we find $\sum m_{\nu }<1.0\mathrm{}$ (respectively, 0.6) eV (at $2\sigma ),$ using only CMB and LSS data (respectively, including priors from supernova data and the HST Key Project), a bound that is quite insensitive to the splitting of the total mass between the three species. When the total number of neutrinos or relativistic relics, $N_{\mathrm{eff}},$ is left free, the upper bound on $\sum m_{\nu }$ (at $2\sigma ,$ including all priors) ranges from 1.0 to 1.5 eV depending on the mass splitting. We provide an explanation of the parameter degeneracy that allows larger values of the masses when $N_{\mathrm{eff}}$ increases. Finally, we show that the limit on the total neutrino mass is not significantly modified in the presence of primordial gravitational waves, because current data provide a clear distinction between the corresponding effects.