Mini-review on the production of Primordial Black Holes fromFirst-Order Phase Transitions in the Early Universe

Primordial black holes (PBHs) can provide a possible connection between the physics of the early Universeand the dark matter. Among the various PBH formation mechanisms, cosmological first-order phase transitions (FOPTs) can generate PBHs through density perturbations arising from the stochastic nucleation oftrue-vacuum bubbles. In this mini-review, we focus on PBH formation from delayed false-vacuum decayduring slow and strongly supercooled FOPTs. We first review how stochastic bubble nucleation can generate non-Gaussian density perturbations and how these perturbations can lead to PBH formation and anextended PBH mass function. Wethendiscussagaugeinconsistency in the conventional treatment, arisingfrom combining density perturbations and the PBH collapse threshold defined in different gauges, and itsimplications for the predicted PBH abundance. Finally, we discuss delayed reheating and the possibility ofan intermediate early matter-dominated epoch as a potential way to revive PBH formation, and highlightthe remaining theoretical uncertainties and future directions