Dynamical Vacuum Compressibility of Space

TL;DR

This paper investigates the quantum thermodynamic properties of space by deriving the vacuum compressibility in various dynamical spacetimes with quantum fields, exploring effects like particle creation and the Casimir effect.

Contribution

It extends previous work by deriving vacuum compressibility for multiple dynamical spacetimes with quantum fields, including backreaction effects and complex vacuum energy behaviors.

Findings

Derived vacuum compressibility for different spacetime geometries.

Analyzed effects of particle creation, Casimir effect, and trace anomaly.

Discussed subtleties in vacuum energy and negative pressures.

Abstract

This paper continues the investigation initiated in arXiv:2204.08634 into the quantum thermodynamic properties of space by deriving the vacuum compressibility of a variety of dynamical spacetimes containing massive and massless conformally coupled quantum fields. The quantum processes studied here include particle creation, Casimir effect, and the trace anomaly. The spaces include $S^2, S^3$, and $T^3$ with prescribed time evolution and $S^1$, where the temporal developments are backreaction determined. Vacuum compressibility belongs to the same group of quantum thermodynamic / mechanical response functions as vacuum viscosity, a concept first proposed in 1970 by Zel'dovich for capturing the effects of vacuum particle production on the dynamics of the early universe, made precise by rigorous work of many authors in the following decade using quantum field theory in curved spacetime methodologies and semiclassical gravity theory for treating backreaction effects. Various subtleties in understanding the behavior of the vacuum energies of quantum field origins, negative pressures and novel complicated features of dynamical compressibility are discussed.