The coincidence limit of the graviton propagator in de Donder gauge on de Sitter background

Abstract

We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.

Graviton propagator in a general invariant gauge on de Sitter

“…The propagator i∆ N (x; x ′ ) has a gauge dependent mass-squared and breaks de Sitter invariance for β < 2. This is in agreement with a previous result [17] where explicit results were obtained for the de Sitter breaking part of the graviton propagator with β = 1.…”

“…For general β, the spin zero projector is (51) and the spin zero structure function is (72). Scalar propagators break de Sitter invariance for any M spin two structure function (72) involves differences of scalar propagators for M 2 S = 0 and M 2 S = (D − 2)H 2 , and it has been shown that its de Sitter breaking persists even after the spin two projectors (54) have been acted [17]. Hence the phenomenon of de Sitter breaking is universal.…”

“…For the case of β = 1 it has been shown that acting the spin zero projectors annihilates the universal de Sitter breaking from the M 2 S = −DH 2 propagator [17], and relation (52) reveals that this remains true for all β. So the spin zero part of the propagator is de Sitter invariant for β > 2.…”

“…The more reliable procedure for exact gauge conditions is to construct the propagator directly. This has recently been accomplished [16,17] for de Donder gauge,…”

Perturbative quantum gravity comes of age

“…Although B W corresponds to a tachyonic mass of m 2 = −DH 2 , it turns out that this source of de Sitter breaking drops out when acted upon by the projectors. 203 The index b N corresponds to a scalar of mass m 2 = −2(…”