Primordial black holes from an interrupted phase transition

TL;DR

This work introduces a novel PBH formation channel wherein an interrupted heating-phase transition occurs during matter-dominated reheating after inflation. Bubbles nucleate as the temperature rises to $T_{ m max}$ but do not complete due to insufficient nucleation rate, expand up to $T_c$, then shrink, leaving macroscopic overdense regions that accrete reheaton matter and collapse into PBHs through a post-collapse accretion phase. The final PBH mass is controlled by the Hubble mass at reheating, making the outcome largely independent of the detailed transition dynamics, while the PBH abundance is tied to the bubble nucleation rate at $T_{ m max}$ and can be substantial for large $\hat{\beta}_{\rm max}$. This mechanism yields a potentially observable PBH population that could contribute to dark matter within existing astrophysical and cosmological constraints, offering a distinct link between early-Universe phase transitions and PBH phenomenology.

Abstract

We propose a new mechanism of primordial black hole formation via an interrupted phase transition during the early matter-dominated stage of reheating after inflation. In reheating, induced by the decay of a pressureless fluid dominating the Universe at the end of inflation, dubbed as reheaton, the temperature of the radiation bath typically increases, reaching a maximum temperature $T_{\rm max}$, and then decreases. We consider a first-order phase transition induced by the increase of the temperature that is aborted as $T_{\rm max}$ is higher than the critical temperature but not sufficiently high for the bubble nucleation rate to overcome the expansion of the Universe. Although bubbles never fully occupy the space, some may be nucleated and expand until the temperature once again decreases to the critical temperature. We argue that these bubbles shrink and disappear as the temperature drops further, leaving behind macroscopic spherical regions with positive density perturbations. These perturbed regions accrete the surrounding matter (reheatons) and eventually collapse into primordial black holes whose mass continues to grow until the onset of radiation domination. We estimate the abundance of these primordial black holes in terms of the bubble nucleation rate at $T_{\rm max}$, and demonstrate that the abundance can be significantly large from a phenomenological perspective.

Figures (7)

• Figure 1: An example of the temperature dependence of scalar potential.
• Figure 2: A schematic chronology of our PBH formation scenario. A symmetry-restoring bubble nucleates at around $a_{\rm max}$ and expands with the bubble wall indicated by the blue line. At $a_{c,2}$, the bubble wall stops expanding, turns around, and shrinks until it completely disappears at $a_{\rm zero}$. This leaves a spherical overdense region of macroscopic size (dashed blue line). This region accretes surrounding matter (reheaton), and the accretion collapses into a PBH via the post-collapse accretion mechanism at $a_{\rm BH}$. The PBH mass grows until the radiation domination starts at $a_{\rm RH}$.
• Figure 3: Fraction of the dark matter relic density that is composed of PBHs, as a function of the PBH mass or equivalently the reheating temperature, using the benchmark values $\alpha=0.1$, $a_{\rm RH}/a_{\rm max}=10$ and $\hat{\beta}_{\rm max}=10^5$. Shaded areas correspond to regions of the parameter space excluded by BBN, CMB anisotropies, cosmic-ray detection, microlensing, gravitational wave detection and accretion (as reported in Carr:2020goxCarr:2009jm).
• Figure 4: $T_c/T_1$ (left) and corresponding $(a_{\rm max}/a_{c,2})_{\rm min}$ (right) are depicted when fermions are introduced with Yukawa interactions. Gauge coupling is chosen such that $\beta_\lambda =10^{-3}$.
• Figure 5: Our numerical result of $S_3/T$ and $\hat{\beta}=-\mathrm{d}(S_3/T)/\mathrm{d} \ln T$ for the Abelian Higgs model. Here, we take $y=0$.