Gravitational waves from vacuum first order phase transitions II: from thin to thick walls

TL;DR

This paper investigates how the thickness of bubble walls in vacuum first-order phase transitions affects the gravitational wave spectrum, suggesting potential to infer the underlying potential from observed spectra.

Contribution

It extends previous simulations by analyzing the impact of bubble wall thickness on gravitational wave spectra in a toy model.

Findings

The peak of the gravitational-wave spectrum varies slightly with wall thickness.

The UV power law becomes steeper as the wall thickness parameter decreases.

Potential to determine the effective potential form from gravitational-wave observations.

Abstract

In a vacuum first-order phase transition, gravitational waves are generated from collision of bubbles of the true vacuum. The spectrum from such collisions takes the form of a broken power law. We consider a toy model for such a phase transition, where the dynamics of the scalar field depends on a single parameter $\overline{\lambda}$, which controls how thin the bubble wall is at nucleation and how close to degenerate the vacua are relative to the barrier. We extend on our previous work by performing a series of simulations with a range of $\overline{\lambda}$. The peak of the gravitational-wave power spectrum varies by up to a factor of $1.3$, which is probably an unobservable effect. We find that the ultraviolet (UV) power law in the gravitational-wave spectrum becomes steeper as $\overline{\lambda} \rightarrow 0$, varying between $k^{-1.4}$ and $k^{-2.2}$ for the $\overline{\lambda}$ considered. This provides some evidence that the form of the underlying effective potential of a vacuum first-order phase transition could be determined from the gravitational-wave spectrum it produces.