  We compute exact expressions of the noise kernel, defined as the expectation
value of the symmetrized connected stress energy bitensor, for
conformally-invariant scalar fields with respect to the conformal vacuum, valid
for an arbitrary separation (timelike, spacelike and null) of points in a class
of conformally-flat spacetimes. We derive explicit expressions for the noise
kernel evaluated in the static de Sitter coordinates with respect to the
Gibbons-Hawking vacuum and analyze the behavior of the noise kernel in the
region near the cosmological horizon. We develop a quasi-local expansion near
the cosmological horizon and compare it with the exact results. This gives
insight into the likely range of validity of the quasi-local approximation
expressions for the noise kernel for the conformally invariant scalar field in
Schwarzschild spacetime which are given in PHYSICAL REVIEW D{\bf 85}, 044037
(2012).
