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 Neff in a general cosmology. We find that Neff= 4.31 with a 95 per cent confidence limit 1.6 ≤Neff≤ 7.1. If we include the H0 prior from the HST project we find the best fit Neff= 4.08 and 1.90 ≤Neff≤ 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 Neff, 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.