Impact of neutrino properties on the estimation of inflationary parameters from current and future observations

We study the impact of assumptions about neutrino properties on the estimation of inflationary parameters from cosmological data, with a specific focus on the allowed contours in the ns/r plane, where ns is the scalar spectral index and r is the tensor-to-scalar ratio. We study the following neutrino properties: (i) the total neutrino mass Mν=a imi (where the index i=1, 2, 3 runs over the three neutrino mass eigenstates); (ii) the number of relativistic degrees of freedom Neff at the time of recombination; and (iii) the neutrino hierarchy. Whereas previous literature assumed three degenerate neutrino masses or two massless neutrino species (approximations that clearly do not match neutrino oscillation data), we study the cases of normal and inverted hierarchy. Our basic result is that these three neutrino properties induce <1σ shift of the probability contours in the ns/r plane with both current or upcoming data. We find that the choice of neutrino hierarchy (normal, inverted, or degenerate) has a negligible impact. However, the minimal cutoff on the total neutrino mass Mν,min=0 that accompanies previous works using the degenerate hierarchy does introduce biases in the ns/r plane and should be replaced by Mν,min=0.059 eV as required by oscillation data. Using current cosmic microwave background (CMB) data from Planck and Bicep/Keck, marginalizing over the total neutrino mass Mν and over r can lead to a shift in the mean value of ns of ∼0.3σ toward lower values. However, once baryon acoustic oscillation measurements are included, the standard contours in the ns/r plane are basically reproduced. Larger shifts of the contours in the ns/r plane (up to 0.8σ) arise for nonstandard values of Neff. We also provide forecasts for the future CMB experiments Cosmic Origins Explorer (COrE, satellite) and Stage-IV (ground-based) and show that the incomplete knowledge of neutrino properties, taken into account by a marginalization over Mν, could induce a shift of ∼0.4σ toward lower values in the determination of ns (or a ∼0.8σ shift if one marginalizes over Neff). Comparison to specific inflationary models is shown. Imperfect knowledge of neutrino properties must be taken into account properly, given the desired precision in determining whether or not inflationary models match the future data.