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.
