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.

💡 Research Summary

The paper investigates the production of primordial black holes (PBHs) and stochastic gravitational‑wave (GW) backgrounds from a first‑order phase transition in the early Universe, emphasizing the importance of going beyond the usual linear approximation of the bubble nucleation rate. Traditionally, the nucleation rate is modeled as Γ∝e^{βt}, retaining only the first‑order term in the expansion of the Euclidean action around the nucleation time. The authors show that for slow, strongly supercooled transitions—characterized by modest values of β/H₀ (≲10) and sizable second‑order coefficients γ—the linear approximation fails to capture the dynamics accurately. They therefore adopt a second‑order expansion, \