  We consider the inference of the cosmic radiation density, traditionally
parameterised as the effective number of neutrino species N_eff, 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 N_eff 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
prefers, in the context of a ``vanilla+N_eff'' cosmological model,
1.1<N_eff<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<N_eff<5.8 (95% C.L.) with
3.8 as the best fit. Inclusion of the Lyman-alpha data shifts the preferred
N_eff upwards because the sigma_8 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 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% C.L.) with 3.0 as the best fit.
