Noise and Fluctuations in Semiclassical Gravity

TL;DR

This paper extends semiclassical gravity to include noise and fluctuations using the CTP formalism, linking quantum processes like particle creation and decoherence to spacetime dynamics, with applications in early universe cosmology and black hole thermodynamics.

Contribution

It introduces a Langevin-type framework for semiclassical gravity, incorporating quantum fluctuations and noise, advancing the understanding of quantum effects in gravitational phenomena.

Findings

Derived an expression for the CTP effective action in terms of Bogolubov coefficients.

Showed how noise relates to particle creation fluctuations.

Extended semiclassical gravity to include stochastic fluctuations and noise.

Abstract

We continue our earlier investigation of the backreaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional (IF) method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the backreaction problem, such as particle creation, decoherence and dissipation. We show how noise and fluctuation arise naturally from the CTP formalism. We derive an expression for the CTP effective action in terms of the Bogolubov coefficients and show how noise is related to the fluctuations in the number of particles created. In so doing we have extended the old framework of semiclassical gravity, based on the mean field theory of Einstein equation with a source given by the expectation value of the energy-momentum tensor, to that based on a Langevin-type equation, where the dynamics of fluctuations of spacetime is driven by the quantum fluctuations of the matter field. This generalized framework is useful for the investigation of quantum processes in the early universe involving fluctuations, vacuum stability and phase transtion phenomena and the non-equilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity. \pacs{pacs numbers: 04.60.+n,98.80.Cq,05.40.+j,03.65.Sq}