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 , 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 three 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 k \approx 0.01 - 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 \Sigma m _ { \nu } < 0.18 eV ( at 95 \% confidence level , Planck+BOSS+ H _ { 0 } ) , approximately independent of the assumed primordial power spectrum model .
When allowing for a free effective number of species , N _ { eff } , the joint constraints on \Sigma m _ { \nu } and N _ { eff } 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 .