Gravitational waves from first-order phase transitions: Towards model separation by bubble nucleation rate

TL;DR

This paper analyzes how the gravitational-wave spectrum from bubble collisions during a first-order phase transition depends on the bubble nucleation rate, proposing a method to distinguish different models based on spectral shape deviations.

Contribution

The study provides analytic expressions for the gravitational-wave spectrum with a Gaussian correction to the nucleation rate, enabling model separation based on spectral shape differences.

Findings

Spectral shape deviates by about 10% with Gaussian correction.

Analytic formulas relate spectrum to energy-momentum correlator.

Potential to distinguish models with future detectors.

Abstract

We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor $\left< T(x)T(y) \right>$, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, $\Gamma \propto e^{\beta t}\rightarrow e^{\beta t-\gamma^2t^2}$, under the thin-wall and envelope approximations. Then we quantitatively investigate how the spectrum changes with the size of the Gaussian correction. It is found that the spectral shape shows ${\mathcal O}(10)\%$ deviation from $\Gamma \propto e^{\beta t}$ case for some physically motivated scenarios. We also briefly discuss detector sensitivities required to distinguish different spectral shapes.