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 less than or equal to N-eff less than or equal to 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 less than or equal to N (eff) less than or equal to 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 sigma(8) measurements, together with better independent measurement of H-0, would help in breaking the degeneracies.