  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.
