Impact of Bubble Nucleation History and Friction on Primordial Black Hole Formation

Abstract

Cosmological first-order phase transitions (FOPTs) in the early Universe are an exciting prediction of many beyond the Standard Model scenarios. Owing to the stochastic nature of bubble nucleation, some causal patches may remain trapped in the false vacuum long after the surrounding regions have completed the transition and started to redshift. Under suitable conditions, these delayed patches can become sufficiently overdense to collapse into primordial black holes (PBHs). One therefore expects characteristic parameters, such as the PBH mass and PBH formation time to be sensitive to the underlying phase-transition dynamics. Here, we adopt a model-independent framework with a fixed mean bubble separation scale ($R_*$) to directly compare the impact of exponential and Gaussian nucleation profiles on PBH formation. We further incorporate the effects of friction on the bubble walls arising from interactions with the surrounding plasma. We find that friction significantly modifies the bubble dynamics, leading to significant changes in the PBH mass and formation time for both nucleation histories. Moreover, the stochastic gravitational-wave spectrum generated by the FOPT can provide a complementary probe of the underlying dynamics, allowing the effects of friction on the bubble wall evolution to be distinguished from the frictionless case.