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arxiv: 2605.11332 · v1 · submitted 2026-05-11 · ✦ hep-ph · astro-ph.CO· gr-qc

Recognition: 2 theorem links

· Lean Theorem

Reviving primordial black hole formation in slow first-order phase transitions

Wen-Yuan Ai , Ke-Pan Xie
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:29 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qc
keywords primordial black holesfirst-order phase transitionssupercooled transitionsmatter-dominated eracurvature perturbationsblack hole spins
0
0 comments X

The pith

Slow reheating after supercooled phase transitions revives primordial black hole formation from curvature perturbations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the formation of primordial black holes from large curvature perturbations generated during slow first-order phase transitions. Earlier analyses concluded that the mechanism fails when density contrasts and collapse thresholds are computed consistently in the same gauge. The authors demonstrate that the channel stays viable provided the transition supercools and reheating proceeds slowly enough for the Universe to enter an early matter-dominated era. In that era even modest overdensities grow and collapse, and the resulting black holes carry large spins as a distinctive signature.

Core claim

Large curvature perturbations arise during slow first-order phase transitions. Prior studies indicated that when evaluated consistently, these perturbations do not reach the threshold for collapse into primordial black holes. However, if the transition is supercooled and reheating proceeds slowly, the Universe enters an early matter-dominated era. In this phase, small overdensities grow linearly and can collapse, forming primordial black holes with large spins.

What carries the argument

The early matter-dominated era induced by slow reheating after a supercooled first-order phase transition, which permits the growth and collapse of small overdensities from curvature perturbations into primordial black holes.

If this is right

  • The mechanism of primordial black hole production from curvature perturbations during slow first-order phase transitions remains viable.
  • Black holes formed this way are produced with large spins.
  • Formation occurs during an early matter-dominated era rather than radiation domination.
  • The scenario links phase-transition dynamics directly to the spin distribution of primordial black holes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Spin measurements of any detected primordial black hole population could distinguish this channel from others.
  • The mass function of black holes may be altered by the duration of the matter-dominated phase.
  • The same supercooling and slow reheating would affect the gravitational-wave spectrum produced by the phase transition.

Load-bearing premise

Reheating after the supercooled transition is sufficiently slow to allow the Universe to enter an early matter-dominated era.

What would settle it

A survey of black hole spins in the mass window expected from an early matter era after a phase transition that finds no excess of high-spin objects would falsify the revived formation channel.

Figures

Figures reproduced from arXiv: 2605.11332 by Ke-Pan Xie, Wen-Yuan Ai.

Figure 1
Figure 1. Figure 1: FIG. 1. PDF of the density contrasts in the comoving volume [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: illustrates the PBH profile for k = 0.9 kmax and TV = 106 GeV. The blue and orange bands show the ranges of Mpbh and fpbh, respectively. In the upper panel, we fix Treh = T max reh while vary β/Hn from 5 to 8. Mpbh lies within 1020 g – 1022 g, an “asteroid-mass” window that can explain all of the dark matter while satisfying current constraints [51– 53], and that could be probed in the future [54–59]. fpbh… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

Large curvature perturbations generated during slow first-order phase transitions are a promising source of primordial black holes. However, recent analyses suggested that the mechanism is ruled out once the density contrast and the formation threshold are evaluated in the same gauge. In this work, we show that this mechanism remains viable: after a supercooled transition, reheating can be sufficiently slow that the Universe enters an early matter-dominated era, during which even small overdensities grow and collapse into primordial black holes. An interesting feature of this scenario is that the black holes are produced with large spins.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that large curvature perturbations from slow first-order phase transitions can still source primordial black holes (PBHs), despite recent gauge-consistent evaluations that appeared to rule out the mechanism. After a supercooled transition, sufficiently slow reheating allows the universe to enter an early matter-dominated era in which even small overdensities grow linearly with the scale factor until they exceed the collapse threshold, forming PBHs that are produced with large spins.

Significance. If the central result holds, the work revives a cosmologically motivated PBH formation channel tied to phase transitions, with potential implications for dark matter and gravitational-wave signals. The distinctive prediction of large PBH spins arising from collapse in the early matter-dominated era offers a falsifiable signature that distinguishes this scenario. The argument relies on standard linear growth during matter domination without introducing new free parameters or ad-hoc fitting.

major comments (2)
  1. [Reheating and early MD era section] The viability of the mechanism rests on reheating after the supercooled transition lasting long enough for linear growth of small initial overdensities (set by the phase-transition curvature spectrum) to reach the collapse threshold. The manuscript provides only order-of-magnitude estimates for the reheating timescale based on false-vacuum energy density and bubble-wall decay rate, without explicit integration of the energy transfer dynamics or a scan over parameter space to confirm that ΔN_MD exceeds ln(δ_c/δ_initial) in viable regions.
  2. [PBH formation and spin estimates] The abstract and concluding claims highlight large PBH spins as an interesting feature, but the spin calculation assumes collapse dynamics in the matter-dominated era without fully incorporating possible angular momentum contributions from the preceding bubble collisions or the phase-transition curvature perturbations themselves.
minor comments (2)
  1. [Introduction] The transition between radiation- and matter-dominated thresholds for collapse should be stated more explicitly when comparing to prior gauge-consistent analyses.
  2. [Perturbation growth] A few equations for the density contrast evolution would benefit from an additional sentence clarifying the gauge choice at each step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the insightful comments. We are pleased that the referee recognizes the potential significance of our results in reviving the PBH formation mechanism from slow first-order phase transitions. We address each of the major comments below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: [Reheating and early MD era section] The viability of the mechanism rests on reheating after the supercooled transition lasting long enough for linear growth of small initial overdensities (set by the phase-transition curvature spectrum) to reach the collapse threshold. The manuscript provides only order-of-magnitude estimates for the reheating timescale based on false-vacuum energy density and bubble-wall decay rate, without explicit integration of the energy transfer dynamics or a scan over parameter space to confirm that ΔN_MD exceeds ln(δ_c/δ_initial) in viable regions.

    Authors: We agree that a more detailed treatment would strengthen the presentation. In the revised manuscript we will add an explicit integration of the energy transfer from false-vacuum energy to radiation, modeling the bubble-wall decay and the resulting reheating history. We will also include a parameter scan over supercooling depth and nucleation rate to demonstrate that ΔN_MD > ln(δ_c/δ_initial) holds throughout the viable region, thereby converting the existing order-of-magnitude argument into a quantitative confirmation. revision: yes

  2. Referee: [PBH formation and spin estimates] The abstract and concluding claims highlight large PBH spins as an interesting feature, but the spin calculation assumes collapse dynamics in the matter-dominated era without fully incorporating possible angular momentum contributions from the preceding bubble collisions or the phase-transition curvature perturbations themselves.

    Authors: We acknowledge that the spin estimates focus on the matter-dominated collapse phase. Bubble collisions and the phase-transition perturbations occur earlier; their angular-momentum contributions are expected to be diluted or randomized during the subsequent prolonged reheating and matter-dominated evolution. To address the referee’s concern we will add a short subsection providing order-of-magnitude estimates of these earlier contributions and showing they remain sub-dominant to the tidal torque acquired during linear growth in the matter-dominated era. This will clarify the robustness of the large-spin prediction without altering the central result. revision: yes

Circularity Check

0 steps flagged

No circularity: standard MD-era growth applied conditionally to supercooled PT without self-referential reduction

full rationale

The paper's central claim is that slow reheating after a supercooled first-order phase transition can produce an early matter-dominated era in which curvature perturbations grow linearly and collapse into PBHs (with large spins). This follows from applying textbook cosmological perturbation theory (δ ∝ a in MD) to the post-transition epoch; the reheating duration is treated as a free parameter range that can be realized in models, not derived or fitted from the paper's own equations. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or description. The argument is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that slow reheating is possible after supercooling, allowing a temporary matter-dominated era; no free parameters or invented entities are indicated in the abstract.

axioms (1)
  • domain assumption Reheating after a supercooled first-order phase transition can be slow enough for the universe to enter an early matter-dominated era.
    This assumption enables overdensity growth and is invoked to revive the formation mechanism.

pith-pipeline@v0.9.0 · 5386 in / 1364 out tokens · 74766 ms · 2026-05-13T01:29:34.825097+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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matches
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supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
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unclear
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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls

    astro-ph.CO 2026-05 unverdicted novelty 6.0

    Tensor perturbations from first-order phase transitions and domain wall annihilation induce curvature fluctuations at second order that form primordial black holes, allowing asteroid-mass PBHs to comprise all dark mat...

Reference graph

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