Black holes and gravitational waves from phase transitions in realistic models

We study realistic models predicting primordial black hole (PBH) formation from density fluctuations generated in a first-order phase transition. We show that the second-order correction in the expansion of the bubble nucleation rate is necessary for accurate predictions and quantify its impact on the abundance of PBHs and gravitational waves (GWs). We find that the distribution of the fluctuations becomes more Gaussian as the second-order term increases. Consequently, models that predict the same PBH abundances can produce different GW spectra.