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 Cosmic Background Imager (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 confidence limit 1.6 <=N_eff<= 7.1. If we include the H₀ prior from the HST project we find the best fit N_eff= 4.08 and 1.90 <=N_eff<= 6.62 for a 95 per cent confidence limit. 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 supernova constraint does not improve the result. We analyse and discuss the degeneracies with other parameters, and point out that probes of the matter power spectrum on smaller scales and accurate independent σ₈ measurements, together with better independent measurement of H₀, would help in breaking the degeneracies.