On gauge dependence of gravitational waves from a first-order phase transition in classical scale-invariant $U(1)'$ models

TL;DR

This paper investigates how gauge choices affect the predicted gravitational wave signals from first-order phase transitions in scale-invariant $U(1)'$ models, revealing significant uncertainties due to gauge artifacts.

Contribution

It demonstrates that thermal resummation introduces gauge dependence in the effective potential, impacting gravitational wave predictions in these models.

Findings

Gauge dependence causes order-of-magnitude uncertainties in gravitational wave spectra.

Thermal resummation breaks the accidental gauge independence of the effective potential.

Predictions vary significantly with gauge choice, affecting the interpretation of gravitational wave signals.

Abstract

We study gauge dependence of gravitational waves produced from a first-order phase transition in classical scale-invariant $U(1)'$ models. Accidental gauge independence of the one-loop effective potential in this class of models is spoiled by including thermal resummation. The gauge artifact in the resummed effective potential propagates to the gravitational wave spectrum and results in one order of magnitude uncertainties in the prediction under a specific gauge choice.