Two loop stress-energy tensor for inflationary scalar electrodynamics

TL;DR

This paper computes the two-loop expectation value of $\langle F_{\mu\nu}F_{\rho\sigma} \rangle$ for inflationary scalar electrodynamics on a de Sitter background and combines it with prior scalar-bilinear results to obtain the full two-loop stress-energy tensor. The authors develop and utilize the de Sitter propagator framework (scalar and vector) in the Schwinger-Keldysh formalism, extracting leading logarithmic contributions that grow as powers of $\ln(a)$ at late times. Their results show explicit agreement with the stochastic formulation's all-orders leading-log resummation, notably yielding a finite, logarithmically enhanced correction to the pressure that drives a secular decrease in the vacuum energy due to inflationary vacuum polarization of charged scalars. The work demonstrates consistency between perturbative two-loop calculations and a nonperturbative stochastic approach, providing a motivated path toward understanding backreaction effects during inflation and the infrared behavior of gauge theories in curved spacetime.

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.

Figures (1)

• Figure 1: Two loop contributions to $\langle \Omega \vert F_{\mu\nu}(x) F_{\rho\sigma}(x) \vert \Omega \rangle$.