Stochastic Gravity: Beyond Semiclassical Gravity

TL;DR

Stochastic gravity extends semiclassical gravity by systematically incorporating quantum fluctuations of matter fields, enabling analysis of metric fluctuations in cosmology and black hole physics beyond linear approximations.

Contribution

It introduces a self-consistent framework for metric fluctuations induced by quantum matter fields, surpassing semiclassical gravity and matching quantum correlation functions at leading order.

Findings

Reproduces quantum correlation functions to leading order in 1/N

Analyzes primordial metric perturbations beyond linear order

Studies horizon fluctuations of evaporating black holes

Abstract

The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by these quantum fluctuations. The correlation functions of the metric fluctuations obtained in stochastic gravity reproduce the correlation functions in the quantum theory to leading order in an 1/N expansion. Two main applications of stochastic gravity are discussed. The first, in cosmology, to obtain the spectrum of primordial metric perturbations induced by the inflaton fluctuations, even beyond the linear approximation. The second, in black hole physics, to study the fluctuations of the horizon of an evaporating black hole.