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 $n_s/r$ plane, where $n_s$ is the scalar spectral index and $r$ is the tensor-to-scalar ratio. We study the following neutrino properties: (i) the total neutrino mass $M_{\nu }=\sum _i{m}_i$ (where the index $i=1$, 2, 3 runs over the three neutrino mass eigenstates); (ii) the number of relativistic degrees of freedom $N_{\mathrm{eff}}$ 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 $<1\sigma$ shift of the probability contours in the $n_s/r$ 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 $M_{\nu ,\min }=0$ that accompanies previous works using the degenerate hierarchy does introduce biases in the $n_s/r$ plane and should be replaced by $M_{\nu ,\min }=0.059\mathrm{eV}$ as required by oscillation data. Using current cosmic microwave background (CMB) data from Planck and Bicep/Keck, marginalizing over the total neutrino mass $M_{\nu }$ and over $r$ can lead to a shift in the mean value of $n_s$ of $\sim 0.3\sigma$ toward lower values. However, once baryon acoustic oscillation measurements are included, the standard contours in the $n_s/r$ plane are basically reproduced. Larger shifts of the contours in the $n_s/r$ plane (up to $0.8\sigma$) arise for nonstandard values of $N_{\mathrm{eff}}$. 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 $M_{\nu }$, could induce a shift of $\sim 0.4\sigma$ toward lower values in the determination of $n_s$ (or a $\sim 0.8\sigma$ shift if one marginalizes over $N_{\mathrm{eff}}$). 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.

• Received 8 November 2016

DOI:https://doi.org/10.1103/PhysRevD.95.043512