Dynamical Vacuum Compressibility of Space

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.
Comment: V2: Added representative references to emergent gravity, highlighting Refs. [43-44] which are closest to the intent of this paper. No alteration of results or derivations from v1