Deducing cosmological observables from the S matrix

Abstract

We study one loop quantum gravitational corrections to the long range force induced by the exchange of a massless scalar between two massive scalars. The various diagrams contributing to the flat space S matrix are evaluated in a general covariant gauge, and we show that dependence on the gauge parameters cancels at a point considerably before forming the full S matrix, which is unobservable in cosmology. It is possible to interpret our computation as a solution to the effective field equations-which could be done even in cosmology-but taking account of quantum gravitational corrections from the source and from the observer.

Graviton propagator in a 2-parameter family of de Sitter breaking gauges

“…where the coefficients of these expansions can be read off by comparing (56) to the power series of the scalar propagators (15)(16)(17),…”

“…In section 2 we generalized the simple gauge condition (2) to a 2-parameter family of gauges (7). The flat space limit of this family coincides with the gauges employed in a study of how source and observer corrections cancel gauge dependence in the effective field equation [16]. In section 3 we argued that just the first order perturbations around the simple gauge provide two thirds of the checks made in that study.…”

“…Even the first order perturbations are very complicated, and we do not advocate using them for routine calculations. Their purpose is to provide an explicit check that our technique for canceling gauge dependence [16] works on de Sitter background. Establishing that fact is crucial, but once it has been done, we expect that future computations will be made using the simple gauge propagator [11,12].…”

“…Note that taking α = β = 1 corresponds to the simple gauge (2), and that taking the flat space limit (H = 0 and a = 1) recovers the family of gauges in which the flat space calculation [16] was made.…”

“…The ∆x-dependent part of (9) follows from the usual procedure of combining denominators, shifting, Wick-rotating and evaluating the Euclidean-space integration, Table 1 concerns gauge dependence in one graviton loop corrections to the effective field equation for a massless, minimally coupled scalar on flat space background [16]. The highly gauge dependent contribution from the 1PI…”