Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space

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 Poincaré 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.

arXiv comment28 pages. Introduction and Discussion sections improved and references added. Published version

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