Strong Supercooling as a Consequence of Renormalization Group Consistency

TL;DR

This paper explores how classical scale invariance influences supercooling during the electroweak phase transition, revealing constraints on scalar couplings and implications for gravitational waves and dark matter.

Contribution

It demonstrates the relationship between scale invariance, supercooling, and Landau pole constraints in minimal models of the electroweak phase transition.

Findings

Supercooling decreases with larger scalar couplings.

Scalar couplings at TeV scale are limited to avoid Landau poles.

Electroweak phase transition is delayed, occurring after the QCD transition.

Abstract

Classically scale-invariant models are attractive not only because they may offer a solution to the long-standing gauge hierarchy problem, but also due to their role in facilitating strongly supercooled cosmic phase transitions. In this paper, we investigate the interplay between these two aspects. We do so in the context of the electroweak phase transition (EWPT) in the minimal scale-invariant theory. We find that the amount of supercooling generally decreases for increasing scalar couplings. However, the stabilization of the electroweak scale against the Planck scale requires the absence of Landau poles in the respective energy range. Scalar couplings at the TeV scale can therefore not become larger than $\mathcal{O}(10^{-1})$. As a consequence, all fully consistent parameter points predict the EWPT not to complete before the QCD transition, which then eventually triggers the generation of the electroweak scale. We also discuss the potential of the model to give rise to an observable gravitational wave signature, as well as the possibility to accommodate a dark matter candidate.