The covariant graviton propagator in de Sitter spacetime

TL;DR

This work addresses the covariant graviton propagator in de Sitter spacetime within a two-parameter gauge and uses an Euclidean $S^4$ framework to derive an explicit Green function. The propagator is decomposed into transverse-traceless, vector, and scalar sectors, with the TT and V parts fixed by mode sums and the scalar sector analyzed in detail, including a gauge choice $\beta=2/3$ that yields compact expressions. Although the covariant propagator exhibits large-distance growth for general gauge parameters, the paper shows that the two-point function of local gauge-invariant quantities remains bounded (and can be arranged to have reduced growth by suitable gauge choices), indicating the growth is a gauge artifact. The results extend previous noncovariant findings and provide explicit, gauge-parameter dependent representations of the covariant propagator, clarifying its physical content and paving the way for further studies of gauge-invariant quantities such as the linearized Weyl tensor.

Abstract

We consider the covariant graviton propagator in de Sitter spacetime in a gauge with two parameters, alpha and beta, in the Euclidean approach. We give an explicit form of the propagator with a particular choice of beta but with arbitrary value of alpha. We confirm that two-point functions of local gauge-invariant quantities do not increase as the separation of the two points becomes large.