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

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 $\overlineλ$, 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 $\overlineλ$. 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 $\overlineλ \rightarrow 0$, varying between $k^{-1.4}$ and $k^{-2.2}$ for the $\overlineλ$ 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.