Numerical simulations of acoustically generated gravitational waves at a first order phase transition

TL;DR

This paper uses numerical simulations to analyze gravitational waves generated by sound waves during a first order phase transition in the early universe, revealing a power-law spectrum and higher energy density than previous models.

Contribution

It demonstrates that sound waves are the dominant source of gravitational waves in such transitions and introduces a dimensionless parameter to quantify acoustic gravitational wave efficiency.

Findings

Sound waves produce a power-law gravitational wave spectrum.

The gravitational wave energy density can be significantly larger than standard predictions.

The efficiency parameter $ ilde ext{Omega}_ ext{GW}$ is approximately 0.8 across simulations.

Abstract

We present details of numerical simulations of the gravitational radiation produced by a first order thermal phase transition in the early universe. We confirm that the dominant source of gravitational waves is sound waves generated by the expanding bubbles of the low-temperature phase. We demonstrate that the sound waves have a power spectrum with a power-law form between the scales set by the average bubble separation (which sets the length scale of the fluid flow $L_\text{f}$) and the bubble wall width. The sound waves generate gravitational waves whose power spectrum also has a power-law form, at a rate proportional to $L_\text{f}$ and the square of the fluid kinetic energy density. We identify a dimensionless parameter $\tilde\Omega_\text{GW}$ characterising the efficiency of this "acoustic" gravitational wave production whose value is $8\pi\tilde\Omega_\text{GW} \simeq 0.8 \pm 0.1$ across all our simulations. We compare the acoustic gravitational waves with the standard prediction from the envelope approximation. Not only is the power spectrum steeper (apart from an initial transient) but the gravitational wave energy density is generically larger by the ratio of the Hubble time to the phase transition duration, which can be 2 orders of magnitude or more in a typical first order electroweak phase transition.