Perturbative gravitational wave predictions for the real-scalar extended Standard Model

TL;DR

This paper provides a detailed perturbative analysis of gravitational wave signals from cosmological phase transitions in a real-scalar extended Standard Model, highlighting the importance of higher-order calculations for accurate predictions.

Contribution

It introduces a comprehensive next-to-next-to-leading order framework using effective field theory for gauge-invariant gravitational wave predictions in this model.

Findings

Perturbative predictions converge well for most parameter points.

Higher-order corrections significantly reduce prediction errors.

Large signals may challenge the validity of perturbative methods.

Abstract

We perform a state-of-the-art study of the cosmological phase transitions of the real-scalar extended Standard Model. We carry out a broad scan of the parameter space of this model at next-to-next-to-leading order in powers of couplings. We use effective field theory to account for the necessary higher-order resummations, and to construct consistent real and gauge-invariant gravitational wave predictions. Our results provide a comprehensive account of the convergence of perturbative predictions for the gravitational wave signals in this model. For the majority of the parameter points in our study, we observe apparent convergence. While leading and next-to-leading order predictions of the gravitational wave amplitude typically suffer from relative errors between $10$ and $10^4$, at next-to-next-to-leading order the typical relative errors are reduced to between $0.5$ and $50$. Nevertheless, for those parameter points predicting the largest signals, potentially observable by future gravitational wave observatories, the validity of the perturbative expansion is in doubt.