Constraints on the cosmic neutrino background

The radiative component of the Universe has a characteristic impact on both large scale structure (LSS) and the cosmic microwave background radiation (CMB). We use the recent WMAP data, together with previous CBI data and 2dF matter power spectrum, to constrain the effective number of neutrino species $N_{eff}$ in a general Cosmology. We find that $N_{eff}=4.31$ with a 95 per cent C.L. $1.6 \le N_{eff} \le 7.1$. If we include the $H_0$ prior from the HST project we find the best fit $N_{eff}=4.08$ and $1.90 \le N_{eff} \le 6.62$ for 95 per cent C.L. The curvature we derive is still consistent with flat, but assuming a flat Universe from the beginning implies a bias toward lower $N_{eff}$, as well as artificially smaller error bars. Adding the Supernovae constraint doesn't improve the result. We analyze and discuss the degeneracies with other parameters, and point out that probes of the matter power spectrum on smaller scales, accurate independent $\sigma_8$ measurements, together with better independent measurement of $H_0$ would help in breaking the degeneracies.