Exact solutions for Vacuum Decay in Unbounded Potentials

TL;DR

This paper derives exact analytical solutions for vacuum decay in unbounded potentials similar to the Higgs potential, revealing thick-wall bubble nucleation and associated spacetime features like horizons and singularities.

Contribution

It provides the first exact solutions for thick-wall bubble nucleation in unbounded potentials, extending previous thin-wall approximations.

Findings

Bubble expansion occurs at asymptotic light speed.

A crunch singularity forms inside the bubble with a surrounding trapped surface region.

An event horizon separates the singularity from the bubble exterior.

Abstract

The Standard Model Higgs potential may become unbounded from below at large field values, with important cosmological implications. For a potential of this form, the commonly assumed scenario of a nucleated thin-wall bubble driving the transition from the electroweak vacuum to the unstable region does not apply. We present exact analytical solutions for potentials that have the same qualitative form as the Higgs potential. They show that the transition is driven by a thick-wall spherical bubble of true vacuum, with a surface that expands at asymptotically the speed of light. A `crunch' singularity appears in the quasi-AdS interior, with the collapsed region also expanding at asymptotically the speed of light. The singularity is surrounded by a region of trapped surfaces whose boundary forms an apparent horizon. An event horizon separates the singularity from the bubble exterior, so that the expansion of the bubble surface is not affected by the collapse of the interior. The solutions provide exact descriptions of the geometry for thick-wall bubbles and are consistent with the analysis of [1,2] for the Higgs potential.