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

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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
Poincare 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.
Original languageEnglish
Article number124006
Pages (from-to)1-30
Number of pages30
JournalPhysical Review D
Publication statusPublished - 2 Jun 2016

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