The Graviton Propagator in de Donder Gauge on de Sitter Background

TL;DR

This work constructs the graviton propagator on a de Sitter background in exact de Donder gauge, showing that de Sitter invariance must be broken by infrared effects, akin to the massless, minimally coupled scalar. The propagator is expressed via covariant projectors acting on scalar structure functions, yielding a spin-zero and a spin-two decomposition that does not assume de Sitter invariance a priori. The scalar equations for these structure functions are solved exactly in a coordinate system that preserves spatial homogeneity and isotropy, with explicit forms that encode de Sitter breaking through infrared behavior. The results aim to simplify renormalization in quantum gravity on inflationary backgrounds and provide a coherent, covariant framework to compare gauges and assess gauge dependence of loop corrections during primordial inflation.

Abstract

We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this propagator than one based on a noncovariant gauge. It remains to be seen how other computational steps compare.