The strongest bounds on active-sterile neutrino mixing after Planck data

Light sterile neutrinos can be excited by oscillations with active neutrinos in the early universe. Their properties can be constrained by their contribution as extra-radiation, parameterized in terms of the effective number of neutrino species N_ eff, and to the universe energy density today \Omega_\nu h^2. Both these parameters have been measured to quite a good precision by the Planck satellite experiment. We use this result to update the bounds on the parameter space of (3+1) sterile neutrino scenarios, with an active-sterile neutrino mass squared splitting in the range (10^{-5} - 10^2 ) eV^2. We consider both normal and inverted mass orderings for the active and sterile states. For the first time we take into account the possibility of two non-vanishing active-sterile mixing angles. We find that the bounds are more stringent than those obtained in laboratory experiments. This leads to a strong tension with the short-baseline hints of light sterile neutrinos. In order to relieve this disagreement, modifications of the standard cosmological scenario, e.g. large primordial neutrino asymmetries, are required.