Quantum Gravitational Effects on Massive Fermions during Inflation

Abstract

We compute the one loop graviton contribution to the self-energy of a very light fermion on a locally de Sitter background. This result can be used to study the effect that a small mass has on the propagation of fermions through the sea of infrared gravitons generated by inflation. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with Bogliubov-Parasuik-Hepp-Zimmermann counterterms. An interesting technical aspect of this computation is the need for two noninvariant counterterms owing to the breaking of de Sitter invariance by our gauge condition.