Cosmological constraints on sterile neutrino oscillations from Planck
  Both particle physics experiments and cosmological surveys can constrain the
properties of sterile neutrinos, but do so with different parameterizations
that naturally use different prior information. We present joint constraints on
the 3$+$1 sterile neutrino model oscillation parameters, $\Delta m_{41}^2$ and
$\sin^22\theta$, with log priors on those parameters using mostly cosmological
data from the Planck satellite. Two cases are considered, one where the sterile
neutrino mixes with electron neutrinos solely, and another where the sterile
neutrino mixes exclusively with muon neutrinos, allowing us to constrain the
mixing angles $\sin^22\theta_{14}$ and $\sin^22\theta_{24}.$ We find that
cosmological data are inconsistent with strong hints of a sterile neutrino
coming from some oscillation channels of the LSND and MiniBooNE experiments,
under the assumption that the sterile neutrinos mix with a single neutrino
flavour. We also forecast the sensitivity with which future CMB experiments
should be able to probe $\Delta m_{41}^2$ and $\sin^22\theta$.
