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 $\sin^22\theta$.