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 .