  We analyze the most recent cosmological data, including Planck, taking into
account the possible existence of a sterile neutrino with a mass at the eV
scale indicated by short-baseline neutrino oscillations data in the 3+1
framework. We show that the contribution of local measurements of the Hubble
constant induces an increase of the value of the effective number of
relativistic degrees of freedom above the Standard Model value, giving an
indication in favor of the existence of sterile neutrinos and their
contribution to dark radiation. Furthermore, the measurements of the local
galaxy cluster mass distribution favor the existence of sterile neutrinos with
eV-scale masses, in agreement with short-baseline neutrino oscillations data.
In this case there is no tension between cosmological and short-baseline
neutrino oscillations data, but the contribution of the sterile neutrino to the
effective number of relativistic degrees of freedom is likely to be smaller
than one. Considering the Dodelson-Widrow and thermal models for the
statistical cosmological distribution of sterile neutrinos, we found that in
the Dodelson-Widrow model there is a slightly better compatibility between
cosmological and short-baseline neutrino oscillations data and the required
suppression of the production of sterile neutrinos in the early Universe is
slightly smaller.
