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

@article{Adams2020DirectCO,
  title={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},
  author={Matthew R. Adams and Fedor Bezrukov and J. Elvin-Poole and Justin J. Evans and P. Guzowski and Br'ian 'O Fearraigh and S. S{\"o}ldner-Rembold},
  journal={arXiv: High Energy Physics - Phenomenology},
  year={2020}
}
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 $\nu_{e}$-disappearance measurements, to a $3+1$ model. This allows us to compare the Planck constraints with those obtained through $\nu_{\mu}\rightarrow\nu_{e}$ appearance… 
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