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

Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes