Comment on "Hearing the signal of dark sectors with gravitational wave detectors" [Phys. Rev. D 94, no. 10, 103519 (2016)]

TL;DR

This paper reevaluates gravitational wave spectra from a scale-invariant SU(2) gauge sector, showing that previous approximations underestimated the true spectra due to inaccuracies in bubble nucleation calculations.

Contribution

It provides a more precise numerical computation of bubble nucleation actions, correcting previous approximations and significantly altering the predicted gravitational wave spectra.

Findings

Previous triangle approximation underestimates action values.

Corrected calculations show different peak frequencies and shapes.

Gravitational wave signals are stronger and more accurately characterized.

Abstract

We revisit the calculation of the gravitational wave spectra generated in a classically scale-invariant $SU(2)$ gauge sector with a scalar field in the adjoint representation, as discussed by J.~Jaeckel, et al. The finite-temperature potential at 1-loop level can induce a strong first-order phase transition, during which gravitational waves can be generated. With the accurate numerical computation of the on-shell Euclidean actions of the nucleation bubbles, we find that the triangle approximation employed by J.~Jaeckel, et al. strongly distorts the actual potential near its maximum and thus greatly underestimates the action values. As a result, the gravitational wave spectra predicted by J.~Jaeckel, et al deviate significantly from the exact ones in peak frequencies and shapes.