Direct comparison of sterile neutrino constraints from cosmological data, νe disappearance data and νμ→νe appearance data in a 3+1 model

We present a quantitative, direct comparison of constraints on sterile neutrinos derived from neutrino oscillation experiments and from Planck data, interpreted assuming standard cosmological evolution. We extend a 1 + 1 model, which is used to compare exclusion contours at the 95% Cl derived from Planck data to those from ν e -disappearance measurements, to a 3 + 1 model. This allows us to compare the Planck constraints with those obtained through ν μ → ν e appearance searches, which are sensitive to more than one active-sterile mixing angle. We find that the cosmological data fully exclude the allowed regions published by the LSND, MiniBooNE and Neutrino-4 collaborations, and those from the gallium and rector anomalies, at the 95% Cl. Compared to the exclusion region from the Daya Bay ν e -disappearance search, the Planck data are more strongly excluding above | Δ m 41 2 | ≈ 0.1 eV 2 and m eff sterile ≈ 0.2 eV , with the Daya Bay exclusion being stronger below these values. Compared to the combined Daya Bay/Bugey/MINOS exclusion region on ν μ → ν e appearance, the Planck data is more strongly excluding above Δ m 41 2 ≈ 5 × 10 - 2 eV 2 , with the exclusion strengths of the Planck data and the Daya Bay/Bugey/MINOS combination becoming comparable below this value.