Graviton propagator in de Sitter space in a simple one-parameter gauge

TL;DR

This work constructs a graviton propagator in de Sitter space within a one-parameter family of noncovariant gauges, controlled by the gauge parameter $\alpha$, to provide a compact, computationally tractable input for inflationary quantum gravity loop calculations. The authors develop a gauge-fixed canonical framework, perform a scalar–vector–tensor decomposition, and solve mode equations in Fourier space, enabling a full graviton two-point function to be expressed in terms of scalar propagators with at most two derivatives acting on them. The resulting closed-form propagator, $i[\Delta]_{\mu\nu}^{ab,\rho\sigma} = i[\Upsilon]_{\mu\nu}^{ab,\rho\sigma} + (1-\alpha) i[\Theta]_{\mu\nu}^{ab,\rho\sigma}$, reduces to the familiar simple-gauge propagator at $\alpha=1$ and respects the Ward–Takahashi identities, making it a powerful tool for gauge-dependence analyses and infrared studies of inflationary observables. The flat-space limit recovers the standard Lorentz-invariant structure, and the formalism accommodates systematic checks of gauge artifacts in secular corrections, supporting robust, gauge-independent physical predictions for cosmological perturbations and quantum gravitational effects during inflation.

Abstract

We construct the graviton propagator in de Sitter space in a one-parameter family of noncovariant gauges. This family generalizes the simple gauge in which most graviton loop computations in de Sitter space have been performed. The resulting propagator has a relatively simple form and will facilitate checks of the gauge dependence of one-loop computations and proposed observables.