A Simple Operator Check of the Effective Fermion Mode Function during Inflation

TL;DR

This paper introduces a simple operator formalism to calculate the leading infrared logarithm of one-loop quantum gravitational corrections to fermion mode functions during inflation, aiming to simplify and sum leading logarithms.

Contribution

It proposes a novel operator rule that reproduces leading infrared effects and could form the basis for a stochastic quantum gravity formulation during inflation.

Findings

The operator rule accurately reproduces the leading infrared logarithm.

The formalism suggests a new approach to summing leading logarithms in quantum gravity.

Spin remains a significant gravitational interaction even at late times.

Abstract

We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.