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arxiv: 2605.15772 · v1 · pith:HVRT3AIFnew · submitted 2026-05-15 · 🌌 astro-ph.CO · hep-ph

Accretion Effects on Primordial Black Hole Reheating Constraints

Chenhuan Wang This is my paper

Pith reviewed 2026-05-20 17:00 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords primordial black holesaccretionreheatingisocurvature gravitational wavesbig bang nucleosynthesismergersearly matter dominationevaporation constraints
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0 comments X

The pith

Accretion onto primordial black holes grows their mass and extends early matter domination, shifting reheating constraints to smaller formation masses and initial abundances.

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

The paper studies how accretion changes the constraints on primordial black holes that could dominate the early universe and reheat it completely through Hawking radiation. Accretion not only increases black hole mass but also lengthens the phase of matter domination before evaporation. This change affects the isocurvature gravitational waves produced at sudden evaporation, and Big Bang nucleosynthesis limits on those waves move the allowed parameter space toward smaller black hole formation masses and smaller initial abundances. The same accretion-driven shifts appear when black holes merge and create broader mass distributions, although the gravitational-wave bounds stay tighter than the merger bounds.

Core claim

Incorporating accretion into the primordial black hole reheating scenario increases black hole masses and prolongs the early matter-dominated era. The modified evolution alters the isocurvature gravitational waves generated right after sudden evaporation, so that Big Bang nucleosynthesis constraints on gravitational-wave energy density permit smaller formation masses and reduced initial abundances. When mergers produce extended mass functions, the allowed parameters undergo comparable shifts, yet the isocurvature gravitational-wave constraints remain stronger than those derived from mergers.

What carries the argument

Accretion-modified primordial black hole mass evolution that lengthens the matter-domination interval and reshapes the spectrum of isocurvature gravitational waves emitted at evaporation.

If this is right

  • Accretion increases black hole mass and extends the duration of early matter domination before evaporation.
  • Big Bang nucleosynthesis limits on isocurvature gravitational waves allow smaller primordial black hole formation masses and smaller initial abundances.
  • Mergers produce extended mass functions and yield similar shifts in the permitted parameter ranges.
  • Isocurvature gravitational-wave constraints stay stronger than constraints obtained from mergers alone.

Where Pith is reading between the lines

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

  • Earlier bounds that omitted accretion may have excluded viable regions of parameter space that become allowed once mass growth is included.
  • Refined accretion modeling could alter the predicted amplitude of early-universe gravitational-wave backgrounds observable by future detectors.
  • Reinterpretation of existing or upcoming primordial gravitational-wave limits may be needed when accretion is taken into account.

Load-bearing premise

Accretion can be added to black hole growth without breaking the sudden-evaporation approximation needed to produce the isocurvature gravitational waves used for the Big Bang nucleosynthesis bound.

What would settle it

A calculation showing that realistic accretion rates prevent the evaporation from remaining sudden enough to generate the modeled isocurvature gravitational waves would invalidate the reported shifts in the allowed parameter space.

read the original abstract

In this work, we study the effects of accretion on the primordial black hole (PBH) reheating scenario. PBHs could form from primordial fluctuations. If they have the right mass and abundance, they could dominate the Universe and complete the reheating entirely through Hawking radiation. We find accretion effects on the BH can not only increase the BH mass, but also prolong such early matter domination. The consequence of the accretion is further investigated using isocurvature induced gravitational waves (GWs), which are generated right after the sudden evaporation of the BHs from the oscillation of the gravitational potential. Big Bang nucleosynthesis limits on the energy density of the GWs put important constraints on the PBH domination scenario. Inclusion of accretion shifts such constraints significantly towards smaller formation mass and smaller initial abundance. Furthermore, the PBH could undergo mergers leading to extended mass functions. We find similar shifts in the allowed parameters with the inclusion of accretion for the merger constraint. We find the constraints from isocurvature GWs typically stronger than the constraints from mergers.

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 manuscript examines the effects of accretion on primordial black hole (PBH) reheating scenarios. PBHs formed from primordial fluctuations can dominate the early universe and reheat it via Hawking radiation. The authors find that accretion increases PBH mass and prolongs the early matter-dominated era. They use isocurvature-induced gravitational waves generated after sudden evaporation to constrain the scenario via Big Bang nucleosynthesis (BBN) limits on GW energy density. Inclusion of accretion shifts the constraints to smaller PBH formation masses and smaller initial abundances. Similar shifts are reported for constraints from PBH mergers leading to extended mass functions. The GW constraints are typically stronger than those from mergers.

Significance. If the central results hold, this work would be significant for updating constraints on PBH parameters in early universe cosmology, particularly by showing how accretion modifies the allowed regions in mass-abundance space. It highlights the importance of including accretion in PBH evolution models for accurate reheating and GW predictions. The comparison between GW and merger constraints provides a useful benchmark. However, the strength is limited by the absence of detailed derivations, error budgets, or quantitative tables in the abstract and available text, making the magnitude of shifts hard to evaluate.

major comments (2)
  1. The central claim relies on applying the sudden-evaporation approximation to compute isocurvature GWs even when accretion is included in the PBH mass evolution equation. Continuous accretion changes the mass continuously, which affects the evaporation rate (∝ M^{-2}) and may violate the condition that evaporation timescale ≪ Hubble time at evaporation. This could smear the gravitational potential oscillation and alter the GW spectrum amplitude and peak frequency. The manuscript does not appear to re-derive the GW transfer function or the suddenness criterion after inserting the accretion term.
  2. The abstract states that accretion increases mass and prolongs domination, leading to shifted constraints, but without explicit equations showing how the accretion rate is modeled (e.g., Bondi accretion or other) or how it is coupled to the Hawking evaporation, it is unclear if the mass evolution is self-consistent or how the duration of the matter era is quantitatively extended.
minor comments (2)
  1. The abstract mentions 'We find similar shifts in the allowed parameters with the inclusion of accretion for the merger constraint' but does not specify the quantitative shift or the details of the extended mass function from mergers.
  2. Clarify the definition of initial abundance and formation mass used in the constraints, perhaps with a table of parameter ranges explored.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for providing constructive comments. We respond to the major comments point by point below.

read point-by-point responses

  1. Referee: [—] The central claim relies on applying the sudden-evaporation approximation to compute isocurvature GWs even when accretion is included in the PBH mass evolution equation. Continuous accretion changes the mass continuously, which affects the evaporation rate (∝ M^{-2}) and may violate the condition that evaporation timescale ≪ Hubble time at evaporation. This could smear the gravitational potential oscillation and alter the GW spectrum amplitude and peak frequency. The manuscript does not appear to re-derive the GW transfer function or the suddenness criterion after inserting the accretion term.

    Authors: We thank the referee for highlighting this important point regarding the validity of the sudden-evaporation approximation. Upon re-examination, the inclusion of accretion does modify the mass history, but for the PBH masses and abundances in our constrained parameter space, the evaporation still proceeds on a timescale much shorter than the Hubble time once it begins to dominate. The gravitational potential oscillations are thus still effectively sudden. We did not re-derive the full GW transfer function because the isocurvature source term is triggered by the rapid disappearance of the PBH density, which remains valid. However, we will add a dedicated subsection justifying the approximation with accretion, including a comparison of timescales. revision: partial

  2. Referee: [—] The abstract states that accretion increases mass and prolongs domination, leading to shifted constraints, but without explicit equations showing how the accretion rate is modeled (e.g., Bondi accretion or other) or how it is coupled to the Hawking evaporation, it is unclear if the mass evolution is self-consistent or how the duration of the matter era is quantitatively extended.

    Authors: We agree that the modeling details should be more explicit. The accretion is modeled using the Bondi rate for PBHs in a radiation background, and the mass evolution equation combines the positive accretion term with the negative Hawking evaporation term. This is solved numerically to determine the duration of matter domination. We will insert the explicit equations into the revised manuscript and add a quantitative illustration of the extended domination period. revision: yes

Circularity Check

0 steps flagged

No significant circularity; constraints rely on external BBN limits

full rationale

The paper models accretion as increasing PBH mass and extending the early matter-dominated era, then applies external BBN bounds on the energy density of isocurvature GWs generated by sudden evaporation. The GW spectrum and BBN limits are treated as independent external inputs rather than quantities fitted or defined inside the paper. No derivation step reduces a reported shift or constraint to a self-fit, self-citation chain, or ansatz smuggled from prior work by the same author. The central results therefore remain self-contained against the stated external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard PBH reheating scenario and external BBN limits; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption PBHs with appropriate mass and abundance can dominate the universe and complete reheating via Hawking radiation
    Explicitly stated as the scenario under study.

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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. Inflaton Accretion onto Primordial Black Holes During Reheating

    astro-ph.CO 2026-05 unverdicted novelty 5.0

    Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.

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