A phase transition model for metric fluctuations in vacuum

TL;DR

This paper models metric fluctuations in vacuum as a phase transition using a scalar ^4 model, showing a transition from smooth to rough vacuum states with critical behavior near the transition point.

Contribution

It introduces a phase transition framework for vacuum metric fluctuations using the scalar ^4 model, linking vacuum roughness to critical phenomena.

Findings

Second order phase transition between smooth and rough vacuum phases

Critical exponent  pprox 0.33 near the transition

Vacuum fluctuations exhibit power-law behavior at criticality

Abstract

Regarding metric fluctuations as generating {\it roughness} on the fabric of the otherwise smooth vacuum, it is shown that in its simplest form, the effect can be described by the scalar $\phi^4$ model. The model exhibits a second order phase transition between a smooth (low-temperature) phase and a rough (high-temperature) one, corroborating the absence of metric fluctuations at low energies. In the rough phase near the critical point, vacuum is characterized by a power-law behavior for the fluctuating field with critical exponent $\beta \approx 0.33$.