Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge

TL;DR

This paper calculates the one-graviton loop correction to vacuum polarization in de Sitter space using a covariant gauge, revealing de Sitter invariance breaking and providing tools for future quantum gravity computations.

Contribution

It introduces the first covariant gauge graviton propagator used for a noncoincident loop calculation in de Sitter space, with detailed renormalization and gauge analysis.

Findings

De Sitter invariance is physically broken by the graviton propagator.

Two structure functions are needed to fully describe the vacuum polarization.

The work provides identities to aid future graviton loop calculations.

Abstract

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.