Mode-sum construction of the covariant graviton two-point function in the Poincar\'e patch of de Sitter space

TL;DR

This paper constructs a covariant graviton two-point function in de Sitter space using mode-sum methods, regularizing IR divergences with a mass term, and analyzes its properties across different gauges and limits.

Contribution

It provides a de Sitter-invariant graviton two-point function in arbitrary gauges, regularized with a Fierz-Pauli mass, and compares results with previous analytic continuation methods.

Findings

Two-point function is de Sitter-invariant and IR finite in the massless limit for certain parameters.

IR divergences depend on gauge parameters and are absent only at specific values in the zero-mass case.

Results agree with some previous analytic continuation approaches but differ in IR divergence strength.

Abstract

We construct the graviton two-point function for a two-parameter family of linear covariant gauges in n-dimensional de Sitter space. The construction is performed via the mode-sum method in the Bunch-Davies vacuum in the Poincar\'e patch, and a Fierz-Pauli mass term is introduced to regularize the infrared (IR) divergences. The resulting two-point function is de Sitter-invariant, and free of IR divergences in the massless limit (for a certain range of parameters) though analytic continuation with respect to the mass for the pure-gauge sector of the two-point function is necessary for this result. This general result agrees with the propagator obtained by analytic continuation from the sphere [Phys. Rev. D 34, 3670 (1986); Class. Quant. Grav. 18, 4317 (2001)]. However, if one starts with strictly zero mass theory, the IR divergences are absent only for a specific value of one of the two parameters, with the other parameter left generic. These findings agree with recent calculations in the Landau (exact) gauge [J. Math. Phys. 53, 122502 (2012)], where IR divergences do appear in the spin-two (tensor) part of the two-point function. However, we find the strength (including the sign) of the IR divergence to be different from the one found in this reference.