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. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole
Highlights
Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am Muhlenberg 1, 14476 Potsdam, Germany
In [316] it was shown that the correlation functions that follow from the Einstein–Langevin equation, which emerges in the framework of stochastic gravity, coincide with that obtained with the usual quantization procedures [270] when both the metric perturbations and the inflaton fluctuations are linearized
We have discussed the problem of the validity of semiclassical gravity, a central issue, which stochastic gravity is in a unique position to address
Summary
Stochastic semiclassical gravity is a theory developed in the 1990s using semiclassical gravity (quantum fields in classical spacetimes, the dynamics of both matter and spacetime are solved self-consistently) as the starting point and aiming at a theory of quantum gravity as the goal. The mathematical properties of this quantity and its physical content in relation to the behavior of fluctuations of quantum fields in curved spacetimes are the central issues of this new theory. Stochastic gravity is the necessary foundation to investigate the validity of semiclassical gravity and the viability of inflationary cosmology based on the appearance and sustenance of a vacuum energy-dominated phase It is a useful beachhead supported by well-established low-energy (sub-Planckian) physics from which to explore the connection with high-energy (Planckian) physics in the realm of quantum gravity. We show the scope of stochastic gravity as follows: Living Reviews in Relativity http://www.livingreviews.org/lrr-2008-3
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