One Loop Corrected Mode Functions for SQED during Inflation

TL;DR

This work computes the one-loop corrections to the inflationary mode functions of a massless, minimally coupled scalar in SQED on a locally de Sitter background, solving the quantum-corrected mode equation in two gauges: a non-de Sitter invariant analogue of Feynman gauge and a de Sitter-invariant Lorentz gauge. Using the Schwinger-Keldysh formalism, they express the effective mode equation with self-mass-squared components $M^2_{++}$ and $M^2_{+-}$ and perform a perturbative analysis to order $e^2$, focusing on late-time behavior to avoid initial-state divergences. In both gauges, they show that an appropriate choice of the finite part of the conformal counterterm cancels significant late-time one-loop corrections, in agreement with all-orders stochastic predictions. The results imply that SQED can be renormalized so inflationary scalar production remains unaltered at one loop, reinforcing the stochastic picture and highlighting the influence of conformal counterterms on infrared dynamics during inflation.

Abstract

We solve the one loop effective scalar field equations for spatial plane waves in massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. The computation is done in two different gauges: a non-de Sitter invariant analogue of Feynman gauge, and in the de Sitter invariant, Lorentz gauge. In each case our result is that the finite part of the conformal counterterm can be chosen so that the mode functions experience no significant one loop corrections at late times. This is in perfect agreement with a recent, all orders stochastic prediction.