Gravitons Enhance Fermions during Inflation

TL;DR

This work analyzes one-loop quantum gravity corrections to massless fermions during inflation by solving the effective Dirac equation on de Sitter space within the Schwinger-Keldysh formalism. The main finding is that at late times a spatial plane wave behaves as if multiplied by a time-dependent field-strength renormalization, $Z_2(t)=1-rac{17}{4\pi} G H^2 \ln(a)+O(G^2)$, indicating infrared logarithms accumulate during inflation. A Hartree approximation reproduces the qualitative trend but with different coefficients, underscoring its limitations. The results highlight how inflationary gravitons can significantly affect fermion propagation through infrared effects, suggesting the need for nonperturbative resummation approaches to determine late-time behavior and potential observational consequences.

Abstract

We solve 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 - \frac{17}{4 π} G H^2 \ln(a) + O(G^2). We show that this also follows from making the Hartree approximation, although the numerical coefficients differ.