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 3 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, \mathrm { min } } = 0.059 \mathrm { eV } as required by oscillation data .
Using current Cosmic Microwave Background ( CMB ) data from Planck and Bicep/Keck ( BK14 ) , 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 towards lower values .
However , once Baryon Acoustic Oscillation ( 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 _ { \mathrm { eff } } .
We also provide forecasts for the future CMB experiments 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 towards 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 .