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arxiv: 2002.12778 · v2 · pith:NW5LR773new · submitted 2020-02-27 · 🌌 astro-ph.CO · gr-qc· hep-ph· hep-th

Constraints on Primordial Black Holes

Bernard Carr , Kazunori Kohri , Yuuiti Sendouda , Jun'ichi Yokoyama This is my paper

Pith reviewed 2026-05-15 02:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-phhep-th
keywords primordial black holesdark matter constraintsHawking radiationgravitational lensingbig bang nucleosynthesisgravitational wavescosmic microwave background
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The pith

Updated limits restrict primordial black holes to a small fraction of the universe's mass across 10^{-5} to 10^{50} g.

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

The paper compiles and refreshes the upper bounds on the fraction of the universe that could have collapsed into primordial black holes over a vast mass range. For black holes below about 10^{15} g, which evaporate via Hawking radiation, the constraints come from their effects on big bang nucleosynthesis, the cosmic microwave background, and gamma-ray backgrounds. For heavier black holes, the limits arise from gravitational lensing, dynamical friction on stars and galaxies, accretion signatures, and gravitational wave production. The work also addresses indirect limits from the amplitude of primordial density fluctuations and shows how the bounds relax when black holes follow an extended mass distribution rather than a single mass. A reader would care because these limits determine whether primordial black holes can explain any part of the dark matter or serve as seeds for cosmic structures.

Core claim

We update the constraints on the fraction of the Universe that may have gone into primordial black holes over the mass range 10^{-5}--10^{50} g. Those smaller than ~10^{15} g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background, the Galactic and extragalactic gamma-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than ~10^{15} g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves.

What carries the argument

Mass-dependent upper limits on the initial PBH collapse fraction beta(m) and the present-day dark matter fraction f_PBH(m), assembled from evaporation products for low masses and gravitational observables for high masses.

If this is right

  • Black holes below 10^{15} g are excluded as the dominant form of dark matter because their evaporation would overproduce background radiation.
  • In the range above 10^{15} g, gravitational lensing and dynamical constraints keep the PBH dark matter fraction below roughly 10 percent in most windows.
  • Even a sub-dominant PBH population can still seed supermassive black holes or contribute to LIGO/Virgo merger rates.
  • An extended mass function broadens the allowed parameter space and permits PBHs to address multiple cosmological roles simultaneously.
  • Second-order gravitational waves and mu-distortions from high-sigma peaks further cap the amplitude of primordial fluctuations that could form PBHs.

Where Pith is reading between the lines

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

  • Improved gravitational wave detectors could directly test the remaining narrow mass windows still compatible with a significant PBH dark matter fraction.
  • Inflationary models that generate large primordial fluctuations must be checked against these PBH bounds to remain viable.
  • Future CMB polarization measurements may tighten the indirect limits from acoustic reheating and thereby shrink the allowed PBH abundance at intermediate masses.

Load-bearing premise

Many of the constraints depend on uncertain details in models of evaporated particle interactions or the precise interpretation of observed radiation backgrounds.

What would settle it

A measured gamma-ray or microlensing event rate exceeding the predicted upper bound in any mass bin where the paper quotes a limit below the observed abundance would directly contradict the constraint for that mass.

read the original abstract

We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range $10^{-5}\text{--}10^{50}$ g. Those smaller than $\sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $\gamma$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $\sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the CDM in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $\mu$-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-$\sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the dark matter, they could play an important cosmological role and provide a unique probe of the early Universe.

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

0 major / 2 minor

Summary. The manuscript updates constraints on the fraction of the Universe in primordial black holes (PBHs) for masses between 10^{-5} and 10^{50} g. It covers evaporation-induced limits for low-mass PBHs from BBN, CMB, gamma-rays and cosmic rays, and relic production, as well as gravitational, lensing, dynamical, accretion and gravitational wave constraints for higher masses. Indirect limits from primordial fluctuations and modifications for extended mass functions are also discussed, with emphasis on observational and theoretical uncertainties.

Significance. This compilation is a valuable reference for the field. By aggregating constraints from diverse observations and flagging uncertainties, it provides a clear overview of the allowed PBH parameter space. The discussion of extended mass functions is particularly useful given the relevance to dark matter, LIGO events and structure formation. The work does not introduce new derivations but faithfully summarizes the literature.

minor comments (2)
  1. [Abstract] Abstract: the evaporation threshold is stated as ~10^{15} g; adding a parenthetical note on the corresponding lifetime (e.g., 'corresponding to the age of the Universe') would improve immediate readability for non-specialist readers.
  2. [Introduction] The paper would benefit from a short table in the introduction that lists the principal constraint categories and the mass ranges they apply to, to help readers navigate the subsequent sections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, their recognition of its value as a reference compilation, and their recommendation to accept. We appreciate the comments on the utility of the extended mass function discussion.

Circularity Check

0 steps flagged

No significant circularity: compilation of independent external constraints

full rationale

The paper aggregates and updates existing constraints on PBH abundance from a wide range of independent observational and theoretical sources (BBN, CMB, gamma-ray backgrounds, lensing, accretion, gravitational waves, etc.) across the stated mass range. It explicitly flags uncertainties in those inputs rather than deriving new results from its own equations or fits. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain; the work functions as a reference summary whose central claims rest on the cited external literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As a review, the claims rest on the validity of cited observational and theoretical results from the literature; no new free parameters, axioms, or invented entities are introduced in this work itself.

axioms (1)
  • standard math Standard cosmological model assumptions underlying BBN, CMB physics, and gravitational lensing calculations
    Invoked throughout when translating observational limits into PBH abundance bounds.

pith-pipeline@v0.9.0 · 5611 in / 1151 out tokens · 41918 ms · 2026-05-15T02:48:55.155179+00:00 · methodology

discussion (0)

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Forward citations

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