One Loop Vaccum Polarization in a Locally de Sitter Background

TL;DR

This paper calculates the one-loop vacuum polarization in massless scalar QED within a de Sitter space, revealing a non-vanishing correction that depends quadratically on the inflationary scale, akin to a photon mass.

Contribution

It provides a fully renormalized one-loop vacuum polarization result in a de Sitter background, explicitly breaking conformal invariance and analyzing its effects on effective field equations.

Findings

One-loop correction depends quadratically on the scale factor.

The correction does not vanish on-shell, indicating a photon mass-like effect.

Conformal anomaly contribution is negligible.

Abstract

We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.