Neutrino mixing and gravitational production via inflation

We develop the Bogolyubov coefficient formalism for gravitational production of fermions with time-dependent mixing, which allows us to study a prototype neutrino system. The neutrino masses and mixings depend on the scalar field values, i.e. the Higgs or singlet scalar expectation values. These are time-dependent in the Early Universe and, due to de Sitter fluctuations, can reach very large values during inflation. As a result, gravitational production of all types of neutrinos can be much enhanced. We obtain an upper bound on the abundance of active and sterile neutrinos produced by classical gravity, $Y\lesssim {10}^{-11}$.