  The simplest inflationary models predict a primordial power spectrum (PPS) of
the curvature fluctuations that can be described by a power-law function that
is nearly scale-invariant. It has been shown, however, that the low-multipole
spectrum of the CMB anisotropies may hint the presence of some features in the
shape of the scalar PPS, which could deviate from its canonical power-law form.
We study the possible degeneracies of this non-standard PPS with the neutrino
anisotropies, the neutrino masses, the effective number of relativistic species
and a sterile neutrino or a thermal axion mass. The limits on these additional
parameters are less constraining in a model with a non-standard PPS when only
including the temperature auto-correlation spectrum measurements in the data
analyses. The inclusion of the polarization spectra noticeably helps in
reducing the degeneracies, leading to results that typically show no deviation
from the $\Lambda$CDM model with a standard power-law PPS.
