Perturbative Quantum Gravity And Newton's Law On A Flat Robertson-Walker Background

TL;DR

This paper derives Feynman rules for gravitons in a flat Robertson-Walker background, computes propagators for different cosmological eras, and evaluates corrections to Newton's law, finding them negligible at small scales.

Contribution

It provides explicit graviton propagators in a cosmological background and analyzes their impact on Newtonian gravity, extending quantum gravity calculations to realistic cosmological settings.

Findings

Corrections to Newton's law are negligible at small scales.

Explicit graviton propagators are derived for inflation, radiation, and matter eras.

Quantum gravity effects are significant only at very large scales.

Abstract

We derive the Feynman rules for the graviton in the presence of a flat Robertson-Walker background and give explicit expressions for the propagator in the physically interesting cases of inflation, radiation domination, and matter domination. The aforementioned background is generated by a scalar field source which should be taken to be dynamical. As an elementary application, we compute the corrections to the Newtonian gravitational force in the present matter dominated era and conclude -- as expected -- that they are negligible except for the largest scales.