Strong supercooling as a consequence of renormalization group consistency

Abstract

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 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.