Quantum corrected geodesics

TL;DR

This paper calculates quantum corrections to classical particle trajectories due to gravitons, showing that quantum effects cause deviations from classical geodesics in specific spacetimes.

Contribution

It introduces a method to compute graviton-induced quantum corrections to test particle motion and demonstrates deviations from classical geodesics in cosmological and lower-dimensional models.

Findings

Quantum corrections modify classical geodesic paths.

In both studied backgrounds, trajectories deviate from classical geodesics.

The effective action incorporates graviton state expectations.

Abstract

We compute the graviton-induced corrections to the trajectory of a classical test particle. We show that the motion of the test particle is governed by an effective action given by the expectation value (with respect to the graviton state) of the classical action. We analyze the quantum corrected equations of motion for the test particle in two particular backgrounds: a Robertson Walker spacetime and a 2+1 dimensional spacetime with rotational symmetry. In both cases we show that the quantum corrected trajectory is not a geodesic of the background metric.