Primordial Black Holes at the Junction

TL;DR

The paper addresses how primordial black holes can form during first-order cosmological phase transitions and how this process links microphysical details to observable gravitational waves and dark matter signatures. It introduces a unified framework based on the Israel junction conditions to track the collapse of false-vacuum patches, including scenarios with energy stored in Fermi-balls and in multiple transitions within a hidden sector. Key contributions include deriving the turning-point dynamics for PBH formation, computing PBH mass spectra $M_{\rm PBH}$ and dark-matter fractions $f_{\rm PBH}$, and predicting correlated gravitational-wave signals across single and multi-transition scenarios, with a treatment of patch survival probability. The findings reveal that PBHs can populate asteroid-mass ranges and produce multi-messenger signals that upcoming detectors like LISA, $\mu$Ares, and DECIGO could probe, while highlighting parameter regions constrained by evaporation and GW observations. Overall, the work provides a general, analytically controlled toolkit to connect hidden-sector phase-transition microphysics to observable PBH and GW signatures.

Abstract

Primordial black holes (PBHs) formed during first-order phase transitions provide a powerful link between the early-universe microphysics and observable signatures today, including dark matter and gravitational waves. In this work we develop a unified description of PBH formation based on the Israel junction conditions, which capture collapse dynamics without relying on conventional overdensity or pressure-balance arguments. As a first application, we show that exotic objects such as Fermi-balls can collapse into PBHs even when most of the vacuum energy is trapped in solitonic cores, leading to a different gravitational-wave signal relative to vacuum-only scenarios. As a second application, we study multiple phase transitions in a hidden sector, which generate correlated gravitational-wave spectra and PBH abundances across transitions. Our framework, while analytically controlled, is broadly applicable to hidden-sector models with general vacuum, radiation, and matter contributions. We present the resulting predictions for PBH mass spectra, dark matter fractions, and gravitational-wave signals, highlighting parameter regions that remain open in current searches and motivating future probes.

Figures (5)

• Figure 1: GW spectrum, $h^2\Omega_{\rm GW}$ vs $f\left[\rm Hz\right]$ for different masses and scales (red, blue and green curves corresponds to $T_0 = 20 \,\rm{MeV}$ and black, gray and violet curves corresponds to $T_0 = 100 \,\rm{MeV}$). All of the six scenarios corresponds to $\rho_V/\rho_{rad} \approx 0.05$. Also shown are the PLIS curves for upcoming experiments LISA (solid gray) and proposed experiments µAres, asteroid laser ranging, and BBO (dashed gray). The PLIS curves for LISA and BBO are adopted from Schmitz:2020sylBatell:2023wdb but scaled to observation times of 3 yrs for LISA Caprini:2019egz and 4 yrs for BBO Crowder:2005nr. The µAres PLIS is taken from Sesana:2019vho, scaled to SNR = 1. For the asteroid ranging proposal, we adopt the strain sensitivity given in Fedderke:2021kuy and calculate the PLIS curve using the procedure outlined in Caprini:2019egz for SNR = 1 with an assumed experiment duration of 7 yrs. For UltimateDECIGO (UDECIGO) we have adopted the PLIS in Braglia:2021fxn. Black dashed lines represent foregrounds from galactic and extragalactic compact binaries (CB)Robson:2018ifkFarmer:2003pa.
• Figure 2: $f_{\rm PBH}$ as a function of $M_{\rm PBH}$ for two different benchmark hidden sector temperature scales and a range of $M_{\rm PBH}$ for each temperature. The mass value is a parameter choice which can be determined by choosing the corresponding value of the other model parameters. This scenario corresponds to hidden sector where the PBH's are sourced from the vacuum energy difference between the false and true vacua. The orange shaded region indicates the exclusion from PBH evaporation constraints Green:2020jor.
• Figure 3: (Left) GW spectrum, $h^2\Omega_{\rm GW}$ vs $f[\rm Hz]$ for the Fermi-ball scenario. Here we have $(\rho_V+\rho_{FB}) / \rho_{rad}\sim0.085$, and $T_0 = 30\,\rm{MeV}$, $\xi = 1$, along with $\rho_{FB}\sim 3\,\rho_V$. (Right) For the Fermi-ball scenario, the red diamond denotes the pure-vacuum case, while the green diamond represents the FB+vacuum case, both corresponding to a PBH mass of $M_{\rm PBH} = 1.06 \times 10^{18}\,\text{g}$.
• Figure 4: (Left) The GW spectrum corresponding to the multiple phases : Phase 1 (red), $\xi = 1$, Phase 3 for for a thermal kick of $\delta =0.2$ (blue) and Phase 3 for a thermal kick of $\delta =0.33$ (green) where $\xi_f = \xi(1+\delta)$ and hidden sector scale $T_0 = 50 \,\rm{MeV}$ and $\rho_V/\rho_{rad} \sim 0.08$ for the three scenarios. (Right) The PBHs produced in the three scenarios, where we match the coloring scheme to the GW signals. The masses of the PBH is $M = 1.8\times10^{18}\,\rm{g}$.
• Figure 5: (Left) The GW spectrum corresponding to fermion trapping (blue) vs pure vacuum (red), where $\xi = 1$, hidden sector scale $T_0 = 30 \,\rm{MeV}$ and $(\rho_\chi+\rho_V)/\rho_{rad} \sim 0.2$ and $\rho_\chi/\rho_V \sim 9$. (Right) The PBH abundance produced from the two scenarios where the red square corresponds to vacuum only and blue square corresponds to trapped fermion in addition to vacuum. The masses of the PBH is $M = 1.3\times10^{18}\,\rm{g}$.