Observational bounds on the cosmic radiation density
Abstract
We consider the inference of the cosmic radiation density, traditionally parameterised as the effective number of neutrino species Neff, from precision cosmological data. Paying particular attention to systematic effects, notably scale-dependent biasing in the galaxy power spectrum, we find no evidence for a significant deviation of Neff from the standard value of Neff0=3.046 in any combination of cosmological data sets, in contrast to some recent conclusions of other authors. The combination of all available data in the linear regime prefers, in the context of a ``vanilla+Neff'' cosmological model, 1.1<Neff<4.8 (95% C.L.) with a best-fit value of 2.6. Adding data at smaller scales, notably the Lyman-alpha forest, we find 2.2<Neff<5.8 (95% C.L.) with 3.8 as the best fit. Inclusion of the Lyman-alpha data shifts the preferred Neff upwards because the sigma8 value derived from the SDSS Lyman-alpha data is inconsistent with that inferred from CMB. In an extended cosmological model that includes a nonzero mass for Neff neutrino flavours, a running scalar spectral index and a w parameter for the dark energy, we find 0.8<Neff<6.1 (95% C.L.) with 3.0 as the best fit.