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We study the impact of assumptions about neutrino properties on theestimation of inflationary parameters from cosmological data, with a specificfocus on the allowed contours in the $n_s/r$ plane. We study the followingneutrino properties: (i) the total neutrino mass $ M_\nu =\sum_i m_i$; (ii) thenumber of relativistic degrees of freedom $N_{eff}$; and (iii) the neutrinohierarchy: whereas previous literature assumed 3 degenerate neutrino masses ortwo massless neutrino species (that do not match neutrino oscillation data), westudy the cases of normal and inverted hierarchy. Our basic result is thatthese three neutrino properties induce $< 1 \sigma$ shift of the probabilitycontours in the $n_s/r$ plane with both current or upcoming data. We find thatthe choice of neutrino hierarchy has a negligible impact. However, the minimalcutoff on the total neutrino mass $M_{\nu,{min}}=0 $ that accompanies previousworks using the degenerate hierarchy does introduce biases in the $n_s/r$ planeand should be replaced by $M_{\nu,min}= 0.059$ eV as required by oscillationdata. 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 areincluded, 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$\sigma$) arisefor nonstandard values of $N_{eff}$. We also provide forecasts for the futureCMB experiments COrE and Stage-IV and show that the incomplete knowledge ofneutrino properties, taken into account by a marginalization over $M_\nu$,could induce a shift of $\sim0.4\sigma$ towards lower values in thedetermination of $n_s$ (or a $\sim 0.8\sigma$ shift if one marginalizes over$N_{eff}$). Comparison to specific inflationary models is shown.

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