  Semiclassical Physics in gravitational scenario, in its first approximation
(1st order) cares only for the expectation value of stress energy tensor and
ignores the inherent quantum fluctuations thereof. In the approach of
stochastic gravity, on the other hand, these matter fluctuations are supposed
to work as the source of geometry fluctuations and have the potential to render
the results from 1st order semiclassical physics irrelevant. We study the
object of central significance in stochastic gravity, i.e. the noise kernel,
for a wide class of Friedmann space-times. Through an equivalence of quantum
fields on de Sitter space-time and those on generic Friedmann universes, we
obtain the noise kernel through the correlators of Stress Energy Tensor (SET)
for fixed co-moving but large physical distances. We show that in many
Friedmann universes including the expanding universes, the initial quantum
fluctuations, the universe is born with, may remain invariant and important
even at late times. Further, we explore the cosmological space-times where even
after long times the quantum fluctuations remain strong and become dominant
over large physical distances, which the matter driven universe is an example
of. The study is carried out in minimal as well as non-minimal interaction
settings. Implications of such quantum fluctuations are discussed.
