Two Loop Scalar Bilinears for Inflationary SQED

TL;DR

This paper calculates one and two loop quantum corrections to gauge-invariant scalar bilinears in massless scalar QED on de Sitter space, confirming stochastic predictions and advancing understanding of quantum effects in inflationary cosmology.

Contribution

It provides the first explicit two-loop computations of scalar bilinear expectation values in inflationary scalar QED, validating stochastic approach predictions.

Findings

Results agree with stochastic predictions at two-loop order

Explicit two-loop corrections to scalar bilinears are obtained

Methodology combines dimensional regularization and Schwinger-Keldysh formalism

Abstract

We evaluate the one and two loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.