An effective stochastic semiclassical theory for the gravitational field

TL;DR

This paper derives an effective stochastic semiclassical gravity theory incorporating matter fluctuations, extending the classical Einstein equations with a stochastic correction for quantum stress-energy effects.

Contribution

It introduces a formal derivation of a stochastic semiclassical gravity theory that includes matter fluctuation back reactions, based on the decoherence mechanism.

Findings

The effective theory combines semiclassical gravity with stochastic corrections.

It accounts for matter stress-energy fluctuations in a systematic way.

The approach supports the classicalization of the gravitational field via decoherence.

Abstract

Assuming that the mechanism proposed by Gell-Mann and Hartle works as a mechanism for decoherence and classicalization of the metric field, we formally derive the form of an effective theory for the gravitational field in a semiclassical regime. This effective theory takes the form of the usual semiclassical theory of gravity, based on the semiclassical Einstein equation, plus a stochastic correction which accounts for the back reaction of the lowest order matter stress-energy fluctuations.