Deducing Cosmological Observables from the S-matrix

TL;DR

This paper calculates one-loop quantum gravitational corrections to long-range forces in flat space, demonstrating gauge independence and discussing implications for cosmological observables.

Contribution

It provides a gauge-invariant computation of quantum gravitational effects on long-range forces and interprets these results within the effective field theory framework applicable to cosmology.

Findings

Gauge dependence cancels before forming the full S-matrix.

Quantum corrections can be incorporated into effective field equations.

Results are relevant for understanding quantum effects in cosmological settings.

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 {\it 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.