Strong Supercooling as a Consequence of Renormalization Group
  Consistency
  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.
