Direct comparison of sterile neutrino constraints from cosmological data, ν_e disappearance data and ν_μ→ ν_e 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 |Δm²₄₁|≈0.1eV² and m^sterile_eff ≈ 0.2eV, 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 Δm²₄₁≈ 5 × 10⁻² eV², with the exclusion strengths of the Planck data and the Daya Bay/Bugey/MINOS combination becoming comparable below this value.