The Graviton Propagator in de Donder Gauge on de Sitter Background

TL;DR

This paper constructs the graviton propagator in de Donder gauge on de Sitter space, revealing it must break de Sitter invariance, and provides explicit solutions suitable for inflationary cosmology.

Contribution

It presents the first explicit construction of the graviton propagator in de Donder gauge on de Sitter background, highlighting its invariance properties and potential advantages for renormalization.

Findings

Propagator must break de Sitter invariance

Explicit solutions preserve spatial homogeneity and isotropy

Potential for simplified renormalization processes

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.