# Vacuum energy decay from a q-bubble

## TL;DR

This paper investigates the dynamics of finite-size $q$-field bubbles in vacuum, showing that small bubbles disperse their vacuum energy completely, while larger ones may undergo gravitational collapse, depending on their size and energy scale.

## Contribution

It provides numerical analysis of $q$-bubble evolution with and without gravity, revealing size-dependent dispersal and collapse behaviors.

## Key findings

- Small bubbles disperse vacuum energy completely.
- Large bubbles can undergo gravitational collapse.
- Vacuum energy dispersal depends on bubble size and energy scale.

## Abstract

We consider a finite-size spherical bubble with a nonequilibrium value of the $q$-field, where the bubble is immersed in an infinite vacuum with the constant equilibrium value $q_{0}$ for the $q$-field (this $q_{0}$ has already cancelled an initial cosmological constant). Numerical results are presented for the time evolution of such a $q$-bubble with gravity turned off and with gravity turned on. For small enough bubbles and a $q$-field energy scale sufficiently below the gravitational energy scale $E_\text{Planck}$, the vacuum energy of the $q$-bubble is found to disperse completely. For large enough bubbles and a finite value of $E_\text{Planck}$, the vacuum energy of the $q$-bubble disperses only partially and there occurs gravitational collapse near the bubble center.