Geodesics, gravitons, and the gauge-fixing problem

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.