State-dependent graviton noise in the equation of geodesic deviation

TL;DR

This paper models how quantum state-dependent graviton noise affects geodesic deviation, providing a stochastic framework for understanding gravitational wave detection in quantum gravitational environments.

Contribution

It introduces a stochastic differential equation approach to describe state-dependent graviton noise in geodesic deviation, extending previous models to include quantum state effects.

Findings

Derived the evolution of the density matrix in a graviton environment

Formulated a stochastic geodesic deviation equation with quantum state-dependent noise

Analyzed the impact of graviton noise on gravitational wave detection

Abstract

We consider an equation of the geodesic deviation appearing in the problem of gravitational wave detection in an environment of gravitons. We investigate a state-dependent graviton noise (as discussed in a recent paper of Parikh,Wilczek and Zahariade) from the point of view of the Feynman integral and stochastic differential equations. The evolution of the density matrix and the transition probability in an environment of gravitons is obtained. We express the time evolution by a solution of a stochastic geodesic deviation equation with a noise dependent on the quantum state of the gravitational field.