Stochastic Inflationary Scalar Electrodynamics

TL;DR

This paper develops a stochastic formulation of scalar quantum electrodynamics in de Sitter space, enabling nonperturbative analysis of infrared effects and confirming that super-horizon photons gain mass during inflation.

Contribution

It introduces a stochastic approach to scalar QED in de Sitter space, allowing summation of leading infrared logarithms and providing explicit late-time behavior results.

Findings

Super-horizon photons acquire a mass squared of about 3.2991 H^2.

Scalar remains perturbatively light with mass squared around 0.8961 3 e^2 H^2/8π^2.

Induced change in cosmological constant is approximately -0.6551 3 G H^4/π.

Abstract

We stochastically formulate the theory of scalar quantum electrodynamics on a de Sitter background. This reproduces the leading infrared logarithms at each loop order. It also allows one to sum the series of leading infrared logarithms to obtain explicit, nonperturbative results about the late time behavior of the system. One consequence is confirmation of the conjecture by Davis, Dimopoulos, Prokopec and Tornkvist that super-horizon photons acquire mass during inflation. We compute a photon mass-suqared of about 3.2991 H^2. The scalar stays perturbatively light with a mass-squared of about 0.8961 3 e^2 H^2/8pi^2. Interestingly, the induced change in the cosmological constant is negative, of about -0.6551 3 G H^4/pi.