Quantum Gravitational Effects on Massive Fermions during Inflation I

TL;DR

This paper calculates how quantum gravitational effects during inflation influence the behavior of very light fermions, revealing the impact of infrared gravitons on fermion propagation in a de Sitter universe.

Contribution

It provides the first detailed one-loop graviton correction to fermion self-energy in de Sitter space, including renormalization with noninvariant counterterms due to gauge choice.

Findings

Quantifies the influence of infrared gravitons on fermion propagation.

Demonstrates the necessity of noninvariant counterterms in de Sitter quantum gravity.

Provides a fully renormalized result applicable to inflationary cosmology.

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 BPHZ 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.