A remarkably simple covariant graviton propagator in (Anti-)de Sitter spacetime

TL;DR

This paper derives simple, covariant graviton and ghost propagators in (Anti-)de Sitter spacetimes, highlighting a special gauge choice that improves infrared behavior and is unique to curved backgrounds.

Contribution

It introduces a novel covariant gauge fixing in (Anti-)de Sitter space that simplifies the graviton propagator and enhances infrared properties, unlike in flat spacetime.

Findings

Derived simple covariant graviton propagators in (Anti-)de Sitter space.

Identified a special gauge condition improving IR behavior.

Demonstrated the gauge's uniqueness to curved spacetimes.

Abstract

We present remarkably simple covariant expressions for the graviton and ghost propagators in Anti-de Sitter and de-Sitter spacetimes valid in any spacetime dimension. In gravity there is a $2$-parameter family of covariant gauge-fixing conditions and the simplification occurs for a special choice of these parameters. In this gauge the graviton propagator satisfies $\nabla^\mu\mu\nabla^\nu\mu \, G_{\mu\nu,\alpha'\beta'}(\mu)=0$, where $\mu$ is the geodesic distance between two points, and this condition implies an improved IR behavior. This gauge choice is not possible in flat spacetime.