Induced quantum metric fluctuations and the validity of semiclassical gravity

Abstract

We propose a criterion for the validity of semiclassical gravity ͑SCG͒ which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation ͑the inhomogeneous term͒. These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Stress tensor fluctuations in de Sitter spacetime

“…The step (i) corresponds to substitute the Wightman function (38) in (53). The result has the form (28), with…”

Self-force with a stochastic component from radiation reaction of a scalar charge moving in curved spacetime

“…Finally, the symmetrized quantum two-point functions of the metric fluctuations h ab can be written in terms of intrinsic fluctuations, representing the dispersion in the initial conditions, and induced fluctuations, encoding the information about the fluctuations of the quantum matter [35]. Just like with the particle motion, one cannot simply use any noise kernel for modeling stochastic metric fluctuations.…”

“…The spacetime is therefore driven by both the quantum expectation value of the renormalized stress tensor and a classical stochastic stress-tensor-like object, ξ ab . For an introduction and review of this subject see [34] and [35] for a discussion of the domain of validity of SSG.…”

One-loop corrections to scalar and tensor perturbations during inflation in stochastic gravity

“…Stochastic gravity was proposed as a means of discussing the behavior of the gravitational field on the sub-Planck scale, which is affected by quantum matter fields [21][22][23][24][25][26][27][28][29][30]. From our naive expectation, on this energy scale, the quantum fluctuation of the matter field may dominate that of the gravitational field.…”