The spectrum of symmetric teleparallel gravity

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.