Charged Scalar Self-Mass during Inflation

TL;DR

This paper calculates the one-loop self-mass of a charged scalar during inflation in de Sitter space, comparing different gauges and confirming de Sitter invariance in the conformally coupled case.

Contribution

It provides the first detailed one-loop self-mass calculation for a charged scalar in de Sitter space using two gauges and confirms invariance properties.

Findings

Derived fully renormalized self-mass expressions in two gauges.

Confirmed de Sitter invariance in the conformally coupled case.

Analyzed the scalar's response to inflationary particle production.

Abstract

We compute the one loop self-mass of a charged massless, minimally coupled scalar in a locally de Sitter background geometry. The computation is done in two different gauges: the noninvariant generalization of Feynman gauge which gives the simplest expression for the photon propagator and the de Sitter invariant gauge of Allen and Jacobson. In each case dimensional regularization is employed and fully renormalized results are obtained. By using our result in the linearized, effective field equations one can infer how the scalar responds to the dielectric medium produced by inflationary particle production. We also work out the result for a conformally coupled scalar. Although the conformally coupled case is of no great physical interest the fact that we obtain a manifestly de Sitter invariant form for its self-mass-squared establishes that our noninvariant gauge introduces no physical breaking of de Sitter invariance at one loop order.