Light sterile neutrinos and inflationary freedom

We perform a cosmological analysis in which we allow the primordial power spectrum of scalar perturbations to assume a shape that is different from the usual power-law predicted by the simplest models of cosmological inflation. We parameterize the free primordial power spectrum with a ''piecewise cubic Hermite interpolating polynomial'' (PCHIP). We consider a 3+1 neutrino mixing model with a sterile neutrino having a mass at the eV scale, which can explain the anomalies observed in short-baseline neutrino oscillation experiments. We find that the freedom of the primordial power spectrum allows to reconcile the cosmological data with a fully thermalized sterile neutrino in the early Universe. Moreover, the cosmological analysis gives us some information on the shape of the primordial power spectrum, which presents a feature around the wavenumber k=0.002 Mpc⁻¹