Revisiting the envelope approximation: gravitational waves from bubble collisions

TL;DR

This paper evaluates the envelope approximation's effectiveness in modeling gravitational waves from early universe bubble collisions, comparing it with large-scale simulations and identifying its limitations.

Contribution

It demonstrates the envelope approximation's validity for certain phase transitions and highlights cases where new modeling techniques are necessary.

Findings

Envelope approximation matches large-scale simulation results when scalar field effects dominate.

Power laws in gravitational wave spectra are independent of nucleation rate.

In other cases, the approximation fails, requiring new modeling approaches.

Abstract

We study the envelope approximation and its applicability to first-order phase transitions in the early universe. We demonstrate that the power laws seen in previous studies exist independently of the nucleation rate. We also compare the envelope approximation prediction to results from large-scale phase transition simulations. For phase transitions where the contribution to gravitational waves from scalar fields dominates over that from the coupled plasma of light particles, the envelope approximation is in agreement, giving a power spectrum of the same form and order of magnitude. In all other cases the form and amplitude of the gravitational wave power spectrum is markedly different and new techniques are required.