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A correspondence between fluctuations of conformally invariant quantum fieldsand that of classical fields finally reducing to perfect fluid matter contentis shown to exist. Previously a similar correspondence between the stresstensors was known and well established in the 70's. Using recent resultsobtained in semiclassical stochastic gravity regarding exact definition andsignificance given to quantum fluctuations of the stress tensor, we obtain thiscorrespondence, which is fundamental to statistical analysis of systems incurved spacetime. This is of immense importance, in that the fluctuations ofstress tensor play a similar central role in stochastic gravity, as that of thestress tensor in classical and semiclassical gravity. A relation between thesemiclassical and classical fluctuations therefore, gives insight to themesoscopic phenomena for gravitating systems and would further enhance theperturbative analysis for cosmological spacetime and astrophysical objects,which is an expansive area of research. Interestingly we see that the quantumfluctuations have a correspondence with covaiances of pressure and density ofthe gravitating system in the stochastic analysis.

Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime