Graviton noise on tidal forces and geodesic congruences

TL;DR

This paper investigates how quantum graviton noise influences tidal forces and geodesic congruences, deriving expressions and estimates for different quantum states and analyzing their effects on spacetime evolution.

Contribution

It introduces a stochastic model for graviton noise effects on point masses and extends the analysis to the impact on geodesic congruences using the Raychaudhuri equation.

Findings

Graviton noise induces measurable fluctuations in tidal forces.

Quantum states like Minkowski and squeezed vacua affect the magnitude of these forces.

Quantum graviton noise influences shear and rotation in geodesic congruences.

Abstract

In this work we continue with our recent study, using the Feynman-Vernon worldline influence action and the Schwinger-Keldysh closed-time-path formalism, to consider the effects of quantum noise of gravitons on the motion of point masses. This effect can be regarded as due to a stochastic tensorial force whose correlator is given by the graviton noise kernel associated with the Hadamard function of the quantized gravitational field. Solving the Langevin equation governing the motion of the separation of two masses, the fluctuations of the separation due to the graviton noise can be obtained for various states of the quantum field. Since this force has the stretching and compressing effects like the tidal force, we can view it as one. We therefore derive the expressions for, and estimate the magnitude of, this tidal force for the cases of the Minkowski and the squeezed vacua. The influence of this force on the evolution of the geodesic congruence through the Raychaudhuri equation is then studied and the effects of quantum graviton noise on the shear and rotation tensors presented.