The spectrum of symmetric teleparallel gravity

TL;DR

This paper derives the exact propagator for the most general infinite-derivative symmetric teleparallel gravity theory, expanding the understanding of non-local, ghost-free modifications of gravity within a flat, torsion-free spacetime.

Contribution

It provides the first derivation of the exact propagator for a broad class of infinite-derivative symmetric teleparallel gravity theories, including non-local, ghost- and singularity-free models.

Findings

Derived the exact propagator for the general infinite-derivative symmetric teleparallel theory.

Identified the theory's relation to non-local, ghost-free gravity models.

Decomposed the action into metric and gauge vector components.

Abstract

General Relativity and its higher derivative extensions have symmetric teleparallel reformulations in terms of the non-metricity tensor within a torsion-free and flat geometry. These notes present a derivation of the exact propagator for the most general infinite-derivative, even-parity and generally covariant theory in the symmetric teleparallel spacetime. The action made up of the non-metricity tensor and its contractions is decomposed into terms involving the metric and a gauge vector field and is found to complement the previously known non-local ghost- and singularity-free theories.