Stochastic semiclassical fluctuations in Minkowski spacetime

TL;DR

This paper derives and solves stochastic semiclassical Einstein equations in Minkowski spacetime, analyzing quantum stress-energy fluctuations and their induced metric perturbations, revealing potential non-perturbative gravitational fluctuation behavior.

Contribution

It provides explicit derivations and solutions for stochastic metric fluctuations caused by quantum fields in Minkowski space, including new results for correlation functions and particle creation effects.

Findings

Explicit two-point correlation functions for metric perturbations.

Evidence of non-perturbative behavior in gravitational fluctuations.

Results for both massless and massive scalar fields.

Abstract

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a ``non-perturbative'' behavior in some characteristic correlation lengths.