Vacuum Instability

TL;DR

This paper explores vacuum instability in higher-dimensional general relativity, linking gauge-dependent cosmological constant variations to a fundamental dynamical relation, suggesting classical vacuum instability with particle production implications.

Contribution

It introduces a gauge-independent relation between changes in the cosmological constant and the action, proposing a new perspective on vacuum instability in higher-dimensional gravity.

Findings

Vacuum is classically unstable under the proposed relation.

The relation is independent of gauge choices and fundamental constants.

Implications include potential particle production from vacuum instability.

Abstract

Following fresh attempts to resolve the problem of the energy density of the vacuum, we reconsider the case where the cosmological constant is derived from a higher-dimensional version of general relativity, and interpret the gauge-dependence of $\Lambda $ as a dynamical effect. This leads to a relation between the change in $\Lambda $ and the line element (action) which is independent of gauge choices and fundamental constants: $d\Lambda ds^{2}=-3$. This implies that the (classical) vacuum is unstable, with implications for particle production.