Weyl fermions of spin \( \frac{1}{2} \) minimally coupled to Einstein’s gravity in 4 dimensions cannot be produced purely gravitationally in an expanding Universe at tree level. Surprisingly, as we showed in a recent letter [1], this changes at gravitational 1-loop when cosmic perturbations, like a gravitational wave background, are present. Such a background introduces a new scale, thereby breaking the fermions’ conformal invariance. This leads to a non-vanishing gravitational self-energy for Weyl fermions at 1-loop and induces their production. In this paper, we present an extended study of this new mechanism, explicitly computing this effect using the in-in formalism. We work in an expanding Universe in the radiation-dominated era as a fixed background. Gravitational wave-induced fermion production has rich phenomenological consequences. Notably, if Weyl fermions eventually acquire mass, and assuming realistic — and potentially detectable — gravitational wave backgrounds, the mechanism can explain the abundance of dark matter in the Universe. More generally, gravitational-wave induced freeze-in is a new purely gravitational mechanism for generating other feebly interacting fermions, e.g. right-handed neutrinos. We show that this loop level effect can dominate over the conventional — tree-level — gravitational production of superheavy fermions in a sizable part of the parameter space (https://github.com/koppj/GW-freeze-in/).
