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, 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.
