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

Noise kernels of stochastic gravity in conformally-flat spacetimes