Tunneling decay of false vortices with gravitation

TL;DR

This paper investigates how false vortices influence the decay of a false vacuum in three-dimensional gravity, revealing that vortices significantly catalyze decay with a tunneling rate half that of traditional bubble nucleation.

Contribution

It introduces a detailed analysis of vortex decay with gravity, including new calculations of tunneling rates and decay channels, extending previous non-gravitational models.

Findings

Vortices have a shorter lifetime than bubbles, significantly affecting vacuum decay.

The tunneling exponent for vortices is half that of Coleman-de Luccia bubbles.

Results recover previous non-gravitational findings in the zero-gravity limit.

Abstract

We study the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in three spacetime dimensions with gravity. The scenario considered is one in which the initial state, rather than being the homogeneous false vacuum, contains false vortices. The question addressed is whether, and, if so, under which circumstances, the presence of vortices has a significant catalyzing effect on vacuum decay. After studying the existence and properties of vortices, we study their decay rate through quantum tunneling using a variety of techniques. In particular, for so-called thin-wall vortices we devise a one-parameter family of configurations allowing a quantum-mechanical calculation of tunneling. Also for thin-wall vortices, we employ the Israel junction conditions between the interior and exterior spacetimes. Matching these two spacetimes reveals a decay channel which results in an unstable, expanding vortex. We find that the tunneling exponent for vortices, which is the dominant factor in the decay rate, is half that for Coleman-de Luccia bubbles. This implies that vortices are short-lived, making them cosmologically significant even for low vortex densities. In the limit of the vanishing gravitational constant we smoothly recover our earlier results for the decay of the false vortex in a model without gravity.