Two Loop Scalar Bilinears for Inflationary SQED

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.