Direct comparison of sterile neutrino constraints from cosmological data, $ν_{e}$ disappearance data and $ν_μ\rightarrowν_{e}$ 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 exclusions 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 $ν_μ\rightarrowν_{e}$ 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 regions from the Daya Bay $ν_{e}$-disappearance search, the Planck data are more strongly excluding above $|Δm^{2}_{41}|\approx 0.1\, \mathrm{eV}^{2}$ and $m_\mathrm{eff}^\mathrm{sterile}\approx 0.2\, \mathrm{eV}$, with the Daya Bay exclusion being stronger below these values. Compared to the combined Daya Bay/Bugey/MINOS exclusion region on $ν_μ\rightarrowν_{e}$ appearance, the Planck data is more strongly excluding above $Δm^{2}_{41}\approx 5\times 10^{-2}\,\mathrm{eV}^{2}$, with the exclusion strengths of the Planck data and the Daya Bay/Bugey/MINOS combination becoming comparable below this value.

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