# Gravitational wave energy budget in strongly supercooled phase transitions

## TL;DR

This paper analyzes gravitational wave production during strong supercooled phase transitions, deriving efficiency factors, using lattice simulations, and comparing models to determine the significance of bubble collisions and plasma sources in GW signals.

## Contribution

It provides new efficiency factors for GW production, clarifies bubble collision dependence via lattice simulations, and compares models to assess their GW signatures.

## Key findings

- Bubble collisions are negligible in the |H|^6 model.
- Bubble collisions can be significant in the $U(1)_{B-L}$ model.
- Sound waves dominate the GW spectrum with turbulence effects becoming relevant off-peak.

## Abstract

We derive efficiency factors for the production of gravitational waves through bubble collisions and plasma-related sources in strong phase transitions, and find the conditions under which the bubble collisions can contribute significantly to the signal. We use lattice simulations to clarify the dependence of the colliding bubbles on their initial state. We illustrate our findings in two examples, the Standard Model with an extra $|H|^6$ interaction and a classically scale-invariant $U(1)_{\rm B-L}$ extension of the Standard Model. The contribution to the GW spectrum from bubble collisions is found to be negligible in the $|H|^6$ model, whereas it can play an important role in parts of the parameter space in the scale-invariant $U(1)_{\rm B-L}$ model. In both cases the sound-wave period is much shorter than a Hubble time, suggesting a significant amplification of the turbulence-sourced signal. We find, however, that the peak of the plasma-sourced spectrum is still produced by sound waves with the slower-falling turbulence contribution becoming important off-peak.