The Quantum-Corrected Fermion Mode Function during Inflation

TL;DR

This paper calculates the one-loop quantum corrections to massless fermions during inflation in de Sitter space, revealing a time-dependent renormalization effect influenced by quantum gravity.

Contribution

It provides a fully renormalized computation of fermion self-energy during inflation, including a noninvariant counterterm due to gauge choice, and solves the effective Dirac equation with quantum gravity corrections.

Findings

Late-time behavior shows a time-dependent field strength renormalization Z_2(t).

Quantum gravity induces a logarithmic correction to fermion propagators during inflation.

Results align qualitatively with Hartree approximation predictions.

Abstract

My project computed the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. I employed dimensional regularization and obtain a fully renormalized result by absorbing all divergences with Bogliubov, Parasiuk, Hepp and Zimmermann (BPHZ) counterterms. An interesting technical aspect of my computation was the need for a noninvariant counterterm, owing to the breaking of de Sitter invariance by our gauge condition. I also solved the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time-dependent field strength renormalization of Z_2(t) = 1 - 17(4 pi) *G H^2 *ln(a) + O(G^2). I showed that this also follows from making the Hartree approximation, although the numerical coefficients differ.