Dark Radiation 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 with respect to the usual power-law, arising from the simplest models of cosmological inflation. We parametrize the primordial power spectrum with a piecewise monotone cubic Hermite function and we use it to investigate how the constraints on the various cosmological parameters change: we find that the obtained limits are relaxed with respect to the power-law case, if CMB polarization data are not included. Moreover, the cosmological analyses provide us some indications about the shape of the reconstructed primordial power spectrum, where we notice possible features around $k\simeq0.002\,\mathrm{Mpc}^{-1}$ and $k\simeq0.0035\,\mathrm{Mpc}^{-1}$. If confirmed in future analyses involving enhanced experimental data, these features suggests that the simplest cosmological inflation models may be incomplete.