Observational bounds on the cosmic radiation density

We consider the inference of the cosmic radiation density, traditionally parametrized as the effective number of neutrino species Ne., 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 Ne. from the standard value of N-eff(0) = 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 favours, in the context of a ' vanilla+ Ne. ' cosmological model, 1.1 < N-eff < 4.8 ( 95% CL) with a best-fit value of 2.6. Adding data at smaller scales, notably the Lyman-alpha forest, we find 2.2 < N-eff < 5.8 ( 95% CL) with 3.8 as the best fit. Inclusion of the Lyman-alpha data shifts the preferred Ne. upwards because the sigma(8) value derived from the SDSS ( Sloan Digital Sky Survey) Lyman- a data is inconsistent with that inferred from the cosmic microwave background. In an extended cosmological model that includes a non- zero mass for N-eff neutrino flavours, a running scalar spectral index and a w parameter for the dark energy, we find 0.8 < N-eff < 6.1 ( 95% CL) with 3.0 as the best.