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We present a quantitative, direct comparison of constraints on sterileneutrinos 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 Planckdata to those from $\nu_{e}$-disappearance measurements, to a $3+1$ model. Thisallows us to compare the Planck constraints with those obtained through$\nu_{\mu}\rightarrow\nu_{e}$ appearance searches, which are sensitive to morethan one active-sterile mixing angle. We find that the cosmological data fullyexclude the allowed regions published by the LSND, MiniBooNE and Neutrino-4collaborations, and those from the gallium and rector anomalies, at the 95% CL.Compared to the exclusion regions from the Daya Bay $\nu_{e}$-disappearancesearch, the Planck data are more strongly excluding above $|\Deltam^{2}_{41}|\approx 0.1\, \mathrm{eV}^{2}$ and$m_\mathrm{eff}^\mathrm{sterile}\approx 0.2\, \mathrm{eV}$, with the Daya Bayexclusion being stronger below these values. Compared to the combined DayaBay/Bugey/MINOS exclusion region on $\nu_{\mu}\rightarrow\nu_{e}$ appearance,the Planck data is more strongly excluding above $\Delta m^{2}_{41}\approx5\times 10^{-2}\,\mathrm{eV}^{2}$, with the exclusion strengths of the Planckdata and the Daya Bay/Bugey/MINOS combination becoming comparable below thisvalue.

european physical journal. c, particles and fields

Direct comparison of sterile neutrino constraints from cosmological  data, $\nu_{e}$ disappearance data and $\nu_{\mu}\rightarrow\nu_{e}$  appearance data in a $3+1$ model