Covariant Vacuum Polarizations on de Sitter Background

TL;DR

This paper derives covariant expressions for one-loop vacuum polarization caused by charged scalars on de Sitter space, exploring different formulations and their implications for photon and graviton self-energies.

Contribution

It introduces two covariant formulations of vacuum polarization on de Sitter space and discusses their implications for photon corrections and graviton self-energy.

Findings

Massless scalars break de Sitter invariance.

Light scalars preserve de Sitter invariance.

Surface integral representation highlights initial state effects.

Abstract

We derive covariant expressions for the one loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter invariant formulation does not seem useful, even when it is possible. Our work has important implications for representations of the graviton self-energy on de Sitter.