A cosmologically viable eV sterile neutrino model

The MiniBooNE collaboration recently released a report claiming have observed an excess of electron and anti-electron neutrino with significance of $4.8 \, \sigma$ C.L. corroborating, in this way, the long-standing LSND anomaly. Combined LSND and MiniBooNE analysis reach a significance of $6.0\, \sigma$ C.L. Such a result, if confirmed by future experiments, will cause considerable impact on particle physics since that such anomalies, when interpreted in terms of neutrino oscillation, require the existence of at least one light sterile neutrino. It happens that, on according to standard scenarios, such light sterile neutrino is incompatible with current cosmological data. In this way, understand these anomalies require an extension of the standard model capable of generating tiny masses for both active and sterile neutrinos and re-conciliates such a result with cosmology. An interesting proposal in this direction involve the existence of a secret sector interacting exclusively with sterile neutrinos. In this work we implement the canonical seesaw mechanism into the standard model in such a way that generates tiny masses to the active and sterile neutrinos and embody a secret sector capable of re-conciliating eV sterile neutrinos with cosmology. As other gains, the scalar content required by the implementation of the mechanism provides contribution to rare lepton decays, may accommodate the $g-2$ of the muon and poses a scalar singlet that may drive inflation through Higgs inflation mechanism without problem with loss of unitarity.