Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity

Abstract

For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained.

References in corpus (7)

• One-loop gravitational wave spectrum in de Sitter spacetime
• Probability distributions for quantum stress tensors in four dimensions
• Riemann correlator in de Sitter including loop corrections from conformal fields
• Cosmological perturbations from stochastic gravity
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
• Noise kernels of stochastic gravity in conformally-flat spacetimes
• The Weyl tensor correlator in cosmological spacetimes

Cited by in corpus (1)

• Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes