Inflationary freedom and cosmological neutrino constraints

The most stringent bounds on the absolute neutrino mass scale come from cosmological data. These bounds are made possible because massive relic neutrinos affect the expansion history of the universe and lead to a suppression of matter clustering on scales smaller than the associated free streaming length. However, the resulting effect on cosmological perturbations is relative to the primordial power spectrum of density perturbations from inflation, so freedom in the primordial power spectrum affects neutrino mass constraints. Using measurements of the cosmic microwave background (CMB), the galaxy power spectrum and the Hubble constant, we constrain neutrino mass and number of species for a model-independent primordial power spectrum. Describing the primordial power spectrum by a 20-node spline, we find that the neutrino mass upper limit is a factor 3 weaker than when a power law form is imposed, if only CMB data are used. The primordial power spectrum itself is constrained to better than 10% in the wave vector range k0. 01-0. 25 Mpc^-1. Galaxy clustering data and a determination of the Hubble constant play a key role in reining in the effects of inflationary freedom on neutrino constraints. The inclusion of both eliminates the inflationary freedom degradation of the neutrino mass bound, giving for the sum of neutrino masses m_<0. 18 eV (at 95% confidence level, Planck+BOSS+H₀), approximately independent of the assumed primordial power spectrum model. When allowing for a free effective number of species, N₄₅₅, the joint constraints on m_ and N₄₅₅ are loosened by a factor 1. 7 when the power law form of the primordial power spectrum is abandoned in favor of the spline parametrization.