A simple operator check of the effective fermion mode function during inflation

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.