  We consider gravitational production of singlet fermions such as sterile
neutrinos during and after inflation. The production efficiency due to
classical gravity is suppressed by the fermion mass. Quantum gravitational
effects, on the other hand, are expected to break conformal invariance of the
fermion sector by the Planck scale-suppressed operators irrespective of the
mass. We find that such operators are very efficient in fermion production
immediately after inflation, generating a significant background of stable or
long-lived feebly interacting particles. This applies, in particular, to
sterile neutrinos which can constitute cold non-thermal dark matter for a wide
range of masses, including the keV scale.
