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

TL;DR

This paper establishes a formal correspondence between matter fluctuations in semiclassical and classical gravity for cosmological spacetimes, advancing understanding of mesoscopic phenomena and backreaction effects.

Contribution

It introduces new relations linking quantum stress tensor fluctuations to effective fluid fluctuations, enhancing perturbative analysis in cosmology and astrophysics.

Findings

Derived relations between scalar field fluctuations and effective fluid stress tensor fluctuations.

Provides a framework for studying backreaction of quantum fluctuations on cosmological perturbations.

Facilitates future kinetic theory approaches based on stochastic fluctuations.

Abstract

A correspondence between fluctuations of non-minimally coupled scalar fields and that of an effective fluid with heat flux and anisotropic stresses, is shown. Though the correspondence between respective stress tensors of scalar fields and fluids is known and widely used in literature, the fluctuations in the two cases still await a formal correspondence and are open to investigation in all details. Using results obtained in the newly established theory of semiclassical stochastic gravity which focuses on the fluctuations of the quantum stress tensor, we show new relations in this regard. This development is expected to give insight to the mesoscopic phenomena for gravitating systems, and enable backreaction studies of the fluctuations on the perturbations of astrophysical objects. Such a development is aimed to enhance the perturbative analysis for cosmological spacetimes and astrophysical objects specifically in the decoherence limit. A kinetic theory, which can be based on stochastic fluctuations vs particle picture in curved spacetime may find useful insights from such correspondences in future work.