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

## TL;DR

This paper establishes a fundamental correspondence between quantum matter fluctuations in semiclassical gravity and classical fluid fluctuations in cosmological spacetime, enhancing understanding of mesoscopic phenomena in gravitating systems.

## Contribution

It introduces a novel link between quantum stress tensor fluctuations and classical matter fluctuations, expanding the theoretical framework of stochastic gravity in cosmology.

## Key findings

- Quantum fluctuations correspond to covariances of pressure and density.
- The correspondence aids in statistical analysis of curved spacetime systems.
- It provides insights into mesoscopic phenomena in gravitating systems.

## Abstract

A correspondence between fluctuations of conformally invariant quantum fields and that of classical fields finally reducing to perfect fluid matter content is shown to exist. Previously a similar correspondence between the stress tensors was known and well established in the 70's. Using recent results obtained in semiclassical stochastic gravity regarding exact definition and significance given to quantum fluctuations of the stress tensor, we obtain this correspondence, which is fundamental to statistical analysis of systems in curved spacetime. This is of immense importance, in that the fluctuations of stress tensor play a similar central role in stochastic gravity, as that of the stress tensor in classical and semiclassical gravity. A relation between the semiclassical and classical fluctuations therefore, gives insight to the mesoscopic phenomena for gravitating systems and would further enhance the perturbative analysis for cosmological spacetime and astrophysical objects, which is an expansive area of research. Interestingly we see that the quantum fluctuations have a correspondence with covaiances of pressure and density of the gravitating system in the stochastic analysis.