Thermalization effects on the dynamics of growing vacuum bubbles

TL;DR

This paper investigates how thermalization and ballistic particle dynamics affect the velocity and evolution of vacuum bubbles, revealing that non-equilibrium effects can significantly slow bubble expansion.

Contribution

It introduces a combined analytical and simulation approach to compare thermal equilibrium and ballistic regimes in vacuum bubble dynamics.

Findings

Ballistic particle effects lead to slower bubble walls.

Non-equilibrium effects are significant in bubble evolution.

Stationary solutions may not be reached in dynamic scenarios.

Abstract

We study the evolution of growing vacuum bubbles. The bubble walls interact with the surrounding fluid and may, consequently, reach a terminal velocity. If the mean free path of the particles in the fluid is much shorter than the bubble wall thickness, the fluid is locally in thermal equilibrium and the wall's terminal velocity can be determined by entropy conservation. On the other hand, if local thermal equilibrium inside the wall cannot be maintained, the wall velocity can be estimated from the pressure impacted by ballistic particle dynamics at the wall. We find that the latter case leads to slightly slower bubble walls. Expectedly, we find the largest differences in the terminal velocity when the fluid is entirely ballistic. This observation indicates that the non-equilibrium effects inside walls are relevant. To study bubble evolution, we perform hydrodynamic lattice simulations in the case of local thermal equilibrium and $N$-body simulations in the ballistic case to investigate the dynamical effects during expansion. Both simulations show that even if a stationary solution exists in theory it may not be reached depending on the dynamics of the accelerating bubble walls.