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

TL;DR

This paper derives conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity, enabling solutions in complex spacetimes based on simpler conformally-related backgrounds, with applications to cosmological models.

Contribution

It introduces a method to transform Einstein-Langevin equations between conformally-related spacetimes, simplifying the analysis of metric fluctuations in complex geometries.

Findings

Derived transformation rules for influence action, stress energy tensor, noise and dissipation kernels.

Facilitated solutions for conformally-flat spacetimes using known Minkowski results.

Discussed the fluctuation-dissipation relation in the context of conformal transformations.

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.