Significance of soft-scale breaking on primordial black hole production in Coleman-Weinberg type supercooling-phase transition

TL;DR

This paper examines how soft-scale breaking terms influence primordial black hole formation during supercooling phase transitions in Coleman-Weinberg models, revealing that small positive or negative terms can significantly alter PBH abundance and expand viable parameter space.

Contribution

It introduces the impact of soft-scale breaking terms on PBH production in CW-type phase transitions, highlighting their role in modifying the phase transition dynamics and PBH abundance.

Findings

Positive soft-scale breaking enhances PBH production.

Negative soft-scale breaking suppresses PBH formation.

Broader parameter space for PBH dark matter models.

Abstract

Ultra-supercooling phase transitions can generate large overdensities in the Universe, potentially leading to the formation of primordial black holes (PBHs), which can also be a dark matter candidate. In this work, we focus on the supercooling phase transition for the scale symmetry breaking based on the effective potential of the Coleman-Weinberg (CW) type. We investigate the effect on the PBH production in the presence of an additional mass term for the CW scalar field, what we call a soft-scale breaking term, which serves as the extra explicit-scale breaking term other than the quantum scale anomaly induced by the CW mechanism. We demonstrate that even a small size of the soft-scale breaking term can significantly affect the PBH production depending on its sign: a positive term slows down the phase transition, thereby enhancing the PBH abundance and improving the model's ability to account for dark matter; in contrast, a negative term suppresses the PBH formation. The inclusion of such soft-scale breaking terms broadens the viable parameter space and increases the flexibility of the framework. We further illustrate our results through two ultraviolet-complete realizations: i) a many-flavor QCD-inspired model as a reference model which can dynamically induce a positive-soft scale breaking; ii) a Higgs portal model with a $B-L$ scalar as the benchmark for the case where a negative-soft scale breaking is induced. Our study would provide a new testable link between PBH dark matter and gravitational wave signatures in the CW-type scenario.