Two loop stress-energy tensor for inflationary scalar electrodynamics

TL;DR

This paper computes the two-loop expectation value of the stress-energy tensor in inflationary scalar electrodynamics on de Sitter space, revealing a secular decrease in vacuum energy due to scalar production.

Contribution

It provides the first two-loop calculation of the stress-energy tensor in this setting, confirming stochastic predictions and linking vacuum polarization to energy decay during inflation.

Findings

Agreement with stochastic formulation for nonperturbative resummation

Demonstrates secular decrease in vacuum energy during inflation

Connects scalar production to vacuum polarization effects

Abstract

We calculate the expectation value of the coincident product of two field strength tensors at two loop order in scalar electrodynamics on de Sitter background. The result agrees with the stochastic formulation which we have developed in a companion paper [2] for the nonperturbative resummation of leading logarithms of the scale factor. When combined with a previous computation of scalar bilinears [1], our current result also gives the two loop stress-energy tensor for inflationary scalar electrodynamics. This shows a secular decrease in the vacuum energy which derives from the vacuum polarization induced by the inflationary production of charged scalars.