Measurements in stochastic gravity and thermal variance

TL;DR

This paper investigates thermal quantum fluctuations of photons in a cosmological setting, analyzing their backreaction on spacetime geometry and quantifying metric perturbation variances relevant for early universe physics.

Contribution

It provides explicit analytic forms of the thermal noise kernel for photons and links these fluctuations to metric perturbations within stochastic gravity, advancing understanding of quantum effects in cosmology.

Findings

Thermal fluctuations induce backreaction effects on spacetime geometry.

Explicit analytic form of the thermal noise kernel for photons.

Thermal variance of metric perturbations quantified in cosmological context.

Abstract

We analyze the thermal fluctuations of a free, conformally invariant, Maxwell quantum field (photon) interacting with a cosmological background spacetime, in the framework of quantum field theory in curved spacetimes and semiclassical and stochastic gravity. The thermal fluctuations give rise to backreaction effects upon the spacetime geometry, which are incorporated in the semiclassical Einstein-Langevin equation, evaluated in the cosmological Friedmann-Lema\^{i}tre-Robertson-Walker spacetime. We first evaluate the semiclassical Einstein equation for the background geometry sourced by the thermal quantum stress-energy tensor. For large enough temperature, the solution is approximated by a radiation-dominated expanding universe driven by the thermal bath of photons. We then evaluate the thermal noise kernel associated to the quantum fluctuations of the photon field using point-splitting regularization methods, and give its explicit analytic form in the limits of large and small temperature, as well as a local approximation. Finally, we prove that this thermal noise kernel corresponds exactly to the thermal variance of the induced fluctuations of the linearized metric perturbation in the local and covariant measurement scheme defined by Fewster and Verch. Our analysis allows to quantify the extent to which quantum fluctuations may give rise to non-classical effects, and thus become relevant in inflationary cosmology.