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

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 ${\mathrm{\nabla }}^{\mu }\mu {\mathrm{\nabla }}^{\nu }\mu G_{\mu \nu ,{\alpha }^{\mathrm{\prime }}{\beta }^{\mathrm{\prime }}}(\mu )=0$, 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.