Recent Advances in Stochastic Gravity: Theory and Issues

Abstract

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. We show how a consistent stochastic semiclassical theory can be formulated as a perturbative generalization of semiclassical gravity which describes the back reaction of the lowest order stress-energy fluctuations. The original approach [1] used in the early investigations leading to the establishment of this field [2] (for a review emphasizing ideas, see [3]) was based on quantum open system concepts (where the metric field acts as the “system” of interest and the matter fields as part of its “environment”) and the influence functional method. Here, following Refs. [4, 5] we first give an axiomatic derivation of the Einstein-Langevin equations and then show how they can also be derived by the original method based on the influence functional. As a first application we solve these equations following Ref. [6], and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations in a Minkowski background.KeywordsMinkowski SpacetimeWightman FunctionNegative Energy DensityCoincident LimitClosed Time PathThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.