Gravitational wave generation from bubble collisions in first-order phase transitions: an analytic approach

TL;DR

This paper introduces an analytic method to estimate gravitational wave signals from bubble collisions during first-order phase transitions, providing formulas for spectrum features without relying on numerical simulations or the envelope approximation.

Contribution

It offers a novel analytic framework for modeling gravitational wave production from bubble collisions, including a bubble velocity power spectrum applicable to different transition types.

Findings

Derived analytical formulas for peak frequency and spectrum shape.

Compared analytic results with numerical estimates, showing good agreement.

Provided a model applicable to both detonations and deflagrations.

Abstract

Gravitational wave production from bubble collisions was calculated in the early nineties using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulae for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.