Gravitational waves from bubble dynamics: Beyond the Envelope

TL;DR

This paper develops an analytic model for gravitational-wave production during cosmic first-order phase transitions, accounting for bubble propagation after collisions, and finds enhanced low-frequency spectra compared to previous approximations.

Contribution

It introduces a modeling approach that goes beyond the envelope approximation, incorporating bubble propagation effects in gravitational-wave spectrum calculations.

Findings

Spectrum grows from f^3 to f^1 at low frequencies

Significant enhancement over the envelope approximation

Spectrum saturation indicates decreased energy-momentum correlation

Abstract

We study gravitational-wave production from bubble dynamics (bubble collisions and sound waves) during a cosmic first-order phase transition with an analytic approach. We first propose modeling the system with the thin-wall approximation but without the envelope approximation often adopted in the literature, in order to take bubble propagation after collisions into account. The bubble walls in our setup are considered as modeling the scalar field configuration and/or the bulk motion of the fluid. We next write down analytic expressions for the gravitational-wave spectrum, and evaluate them with numerical methods. It is found that, in the long-lasting limit of the collided bubble walls, the spectrum grows from $\propto f^3$ to $\propto f^1$ in low frequencies, showing a significant enhancement compared to the one with the envelope approximation. It is also found that the spectrum saturates in the same limit, indicating a decrease in the correlation of the energy-momentum tensor at late times. We also discuss the implications of our results to gravitational-wave production both from bubble collisions (scalar dynamics) and sound waves (fluid dynamics).