Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation

TL;DR

This paper investigates how quantum graviton fluctuations influence the motion of two masses, deriving a stochastic force model and analyzing potential detection methods in space-based interferometers.

Contribution

It extends previous work by including all graviton modes and polarizations, providing a comprehensive analysis of graviton-induced fluctuations on geodesic separation.

Findings

Derived a Langevin equation with graviton noise kernel

Analyzed fluctuations in various quantum states including squeezed states

Discussed prospects for detecting primordial graviton fluctuations with space interferometers

Abstract

In this work we consider the effects of gravitons and their fluctuations on the dynamics of two masses using the Feynman-Vernon influence functional formalism, applied to nonequilibrium quantum field theory and semiclassical stochastic gravity earlier by Calzetta, Hu and Verdaguer [1-3], and most recently, to this problem by Parikh, Wilczek and Zahariade [4-6]. The Hadamard function of the gravitons yields the noise kernel acting as a stochastic tensorial force in a Langevin equation governing the motion of the separation of the two masses. The fluctuations of the separation due to the graviton noise are then solved for various quantum states including the Minkowski vacuum, thermal, coherent and squeezed states. The previous considerations of Parikh et al. are only for some selected modes of the graviton, while in this work we have included all graviton modes and polarizations. We comment on the possibility of detecting these fluctuations in primordial gravitons using interferometors with long baselines in deep space experiments.