[Paper Review] Primordial black holes from bubble collisions during a first-order phase transition

Tae Hyun Jung, Takemichi Okui|arXiv (Cornell University)|Oct 8, 2021

Cosmology and Gravitation TheoriesPhysics and Astronomy21 citations

TL;DR

This paper proposes that primordial black holes (PBHs) can form via collisions of near-horizon-sized bubbles with thick fluid shells during a first-order phase transition in the early universe. Using the hoop conjecture, it shows that such collisions can produce a monochromatic PBH mass spectrum, with abundances potentially reaching dark matter levels or over-closing the universe, depending on model parameters derived from future simulations.

ABSTRACT

We study the possibility of production of primordial black holes (PBHs) from bubble collisions during a first-order phase transition. While typical colliding bubbles are small and irrelevant for PBH production, we find that those that can produce PBHs must have a macroscopically thick fluid shell and have been born much before the typical nucleation time. Particularly large uncertainties arise from an exponential sensitivity of the nucleation rate on the required duration of bubble growth which depends on the details of the collisions and the evolution of the spacetime metric toward the end of the phase transition. We introduce a few parameters to be obtained from future numerical simulation to represent those unknowns, and estimate the PBH abundance in an Abelian Higgs benchmark model and show that it can be significant. We predict an approximately monochromatic PBH mass spectrum, and find regions in the parameter space where the PBHs can constitute entire dark matter or even over-close the universe. Our result thus shows that models with a first-order phase transition can be constrained by over-abundant PBHs or null results of other PBH searches.

Motivation & Objective

• To investigate whether bubble collisions during a first-order phase transition can produce observationally significant primordial black holes (PBHs).
• To identify the physical conditions—specifically near-horizon-sized bubbles with thick fluid shells—necessary for PBH formation.
• To estimate the PBH abundance in a benchmark Abelian Higgs model using the hoop conjecture and numerical parameters from future simulations.
• To assess the cosmological implications of PBH overproduction, including over-closure of the universe or constraints from PBH search null results.
• To provide a framework for testing first-order phase transition models via PBH detection or non-detection.

Proposed method

• Applies the hoop conjecture as a criterion for black hole formation, requiring that 2GM ≳ C_D, where C_D is the largest circumference of a dense region D.
• Models the dense region D formed by colliding bubbles with macroscopically thick fluid shells on the bubble walls, which are essential for sufficient mass concentration.
• Assumes bubble radii are near the horizon size and uses dimensional analysis to relate the critical field value φ_c to temperature T and mass scale μ_*.
• Estimates the bubble nucleation rate Γ_n(T) using thermal instanton methods, with the exponential suppression given by e^(-S_4[φ_c]) and prefactor T^4.
• Converts temperature-dependent rates to time-dependent rates via T(t) = T_n exp(-H(t - t_n)), valid during vacuum-dominated expansion.
• Computes PBH formation probability P_PBH(t) and number density n_PBH via integration of the rate, using parameters like κ, ΔΩ/4π, and g to scale the result.

Experimental results

Research questions

• RQ1 Can bubble collisions during a first-order phase transition produce primordial black holes with observable abundance?
• RQ2 What physical conditions—such as bubble size and shell thickness—are necessary for significant PBH formation?
• RQ3 What is the expected mass spectrum of PBHs formed in such collisions, and is it monochromatic?
• RQ4 How does the PBH abundance depend on model parameters like coupling g, vacuum energy scale μ_*, and solid angle ΔΩ?
• RQ5 Can PBH overproduction from this mechanism constrain or rule out models with first-order phase transitions?

Key findings

• PBHs can form from collisions of near-horizon-sized bubbles with thick fluid shells, satisfying the hoop conjecture condition for black hole formation.
• The resulting PBH mass spectrum is approximately monochromatic, determined by the bubble wall dynamics and energy density compression.
• In the Abelian Higgs benchmark model, PBHs can constitute the entire dark matter density or even over-close the universe, depending on parameters.
• The PBH abundance f_PBH is exponentially sensitive to the solid angle ΔΩ/4π, with suppression for smaller angles.
• The model predicts that future numerical simulations must resolve the fluid shell thickness and wall velocity profile to accurately estimate PBH yields.
• The quantum tunneling contribution to the nucleation rate is negligible compared to the thermal rate, justifying the use of classical thermal instanton estimates.