Geodesics, gravitons and the gauge fixing problem

TL;DR

This paper derives a gauge-invariant quantum-corrected geodesic equation accounting for graviton backreaction, addressing gauge dependence issues in quantum gravity and providing a physically meaningful observable.

Contribution

It introduces a gauge-invariant formulation of the quantum-corrected geodesic equation including graviton backreaction effects.

Findings

The background metric's gauge dependence is problematic for physical interpretation.

The derived geodesic equation is explicitly gauge fixing independent.

The approach offers a physically meaningful observable in quantum gravity.

Abstract

When graviton loops are taken into account, the background metric obtained as a solution to the one-loop corrected Einstein equations turns out to be gauge fixing dependent. Therefore it is of no physical relevance. Instead we consider a physical observable, namely the trajectory of a test particle in the presence of gravitons. We derive a quantum corrected geodesic equation that includes backreaction effects and is explicitly independent of any gauge fixing parameter.