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

Abstract

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. We study the following neutrino properties: (i) the total neutrino mass $ M_\nu =\sum_i m_i$; (ii) the number of relativistic degrees of freedom $N_{eff}$; and (iii) the neutrino hierarchy: whereas previous literature assumed 3 degenerate neutrino masses or two massless neutrino species (that 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 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 $M_{\nu,min}= 0.059$ eV as required by oscillation data. Using current CMB data from Planck and Bicep/Keck, marginalizing over $ M_\nu$ and over $r$ can lead to a shift in the mean value of $n_s$ of $\sim0.3\sigma$ towards lower values. However, once BAO 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 $N_{eff}$. We also provide forecasts for the future CMB experiments COrE and Stage-IV and show that the incomplete knowledge of neutrino properties, taken into account by a marginalization over $M_\nu$, could induce a shift of $\sim0.4\sigma$ towards lower values in the determination of $n_s$ (or a $\sim 0.8\sigma$ shift if one marginalizes over $N_{eff}$). Comparison to specific inflationary models is shown.