Noise kernels of stochastic gravity in conformally-flat spacetimes

TL;DR

This paper derives explicit analytic expressions for the noise kernels of a conformally coupled scalar field in conformally-flat spacetimes, including cosmologically relevant Friedmann-Robertson-Walker universes, within the framework of stochastic gravity.

Contribution

It provides a method to obtain closed-form noise kernels in conformally-flat spacetimes using conformal and coordinate transformations, advancing stochastic gravity calculations.

Findings

Explicit noise kernels in Minkowski, Einstein, and open Einstein spaces.

Closed analytic forms for noise kernels in conformally-flat spacetimes.

Application to Friedmann-Robertson-Walker universes.

Abstract

The central object in the theory of semiclassical stochastic gravity is the noise kernel which is the symmetric two point correlation function of the stress-energy tensor. Using the corresponding Wightman functions in Minkowski, Einstein and open Einstein spaces, we construct the noise kernels of a conformally coupled scalar field in these spacetimes. From them we show that the noise kernels in conformally-flat spacetimes, including the Friedmann-Robertson-Walker universes, can be obtained in closed analytic forms by using a combination of conformal and coordindate transformations.