REVIEW 2 minor 60 cited by
Updated limits restrict primordial black holes to a small fraction of the universe's mass across 10^{-5} to 10^{50} g.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
Updated compilation shows PBHs are tightly constrained across 55 orders of magnitude in mass, ruling out dominant dark matter contributions except in narrow windows, with many limits carrying observational uncertainties.
T0 review reviewed 2026-05-15 challenge →
load-bearing objection A solid update to the standard PBH constraint compilation that organizes limits across 55 orders of magnitude but adds no new derivations.
Constraints on Primordial Black Holes
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
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.
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.
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
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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)
- [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.
- [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
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
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
axioms (1)
- standard math Standard cosmological model assumptions underlying BBN, CMB physics, and gravitational lensing calculations
Cite this review
Pith. "Pith review of Constraints on Primordial Black Holes." pith.science (2026). https://pith.science/paper/NW5LR773
@misc{pith2026200212778,
author = {Pith},
title = {Pith review of: Constraints on Primordial Black Holes},
year = {2026},
howpublished = {\url{https://pith.science/paper/NW5LR773}},
note = {Machine review of arXiv:2002.12778}
}
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.
Forward citations
Cited by 60 Pith papers
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Constraints on the Primordial Black Hole Abundance using Pulsar Parameter Drifts
The first search for scalar-induced gravitational waves via pulsar parameter drifts yields f_PBH < 10^{-10} (95% CL) for PBH masses 0.3 to 4e4 solar masses, strongly disfavoring a primordial black hole origin for LVK ...
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The statistics of curvature-profile dispersion in primordial black hole formation
Rare coherent shape deformations of primordial curvature profiles can dominate primordial black hole abundance by lowering the collapse threshold enough to overcome their Gaussian statistical cost.
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Primordial Black Holes from Vector-Induced Curvature Perturbations Sourced by Primordial Magnetic Fields
Vector modes from primordial magnetic fields remain constant in a kination epoch and source second-order curvature perturbations scaling as P_R(k) ∝ k^{-5}, sufficient for PBH dark matter abundance in a Ratra-type mag...
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Are Primordial Black Holes a Natural Dark Matter Candidate?
PBH dark matter spans all naturalness tiers, with some mechanisms as natural as WIMPs or freeze-in particles, determined by abundance map structure rather than candidate type.
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Hidden-sector accretion and warped black-string seeds for high-redshift supermassive black holes
A warped 5D geometry with hidden-sector accretion produces growing Schwarzschild/Vaidya black-hole seeds on our brane via a common horizon intersection.
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Accretion of Primordial Black Holes in Stellar Interiors
Self-consistent spherical accretion simulations show cooling-enhanced growth of PBHs with radiative efficiency ~10^{-2} in the bremsstrahlung regime, yielding a critical seed mass of ~10^{-16} M_sun to consume a solar...
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Carr criterion and mass gaps in non-singular primordial black hole formation
Non-singular gravity with regulator ℓ induces a PBH mass gap ~c²ℓ/G and a stronger Carr criterion δ_H > 2GM_gap/R_H - 1 when R_H ~ ℓ.
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Gravitational Waves from Black Hole Reheating: The Scalar-Induced Component
Accounting for the minimal mass spread of primordial black holes from gravitational collapse suppresses the Poltergeist GW background to the level of generic scalar-induced signals and reopens ultra-light PBH parameter space.
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Tunneling and tidal stripping in multifield ultralight dark matter halos
A semiclassical tunneling model shows that two-field ultralight DM halos have stability bounds that can be relaxed for some density-mass ratios but become more stringent across much of the parameter space compared to ...
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Reviving primordial black hole formation in slow first-order phase transitions
Primordial black hole formation from slow first-order phase transitions remains viable if slow reheating after supercooling creates an early matter-dominated era allowing small overdensities to grow, producing black h...
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Gravitational wave emission from nonspherical collapse in an early matter-dominated era using N-body simulations
Full numerical N-body treatment is required for reliable gravitational wave predictions from nonspherical collapse in early matter-dominated eras, with resulting spectra mappable to detector sensitivities via horizon ...
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Gravitational-wave lensing beyond rays: a disordered-system approach
A quenched-disorder approach with Schwinger-Keldysh path integrals produces an averaged density matrix for gravitational waves that separates phase-suppressing exponential terms from oscillatory corrections to coheren...
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Microscopic primordial black holes as macroscopic dark matter from large extra dimensions
In the ADD extra-dimension model, microscopic primordial black holes undergo runaway accretion and grow to macroscopic scales, allowing them to comprise all dark matter with initial abundances as low as 10^{-44}.
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Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background
Stupendously large black holes cast shadows on the CMB that rule out masses above 10^17 solar masses within the last scattering surface and limit their density parameter to below 10^-5 for masses 10^15 to 10^18 solar masses.
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Primordial black holes as cosmic accelerators of light dark matter: Novel direct detection constraints
Primordial black hole evaporation generates light fermionic dark matter capable of producing electron recoils in XENONnT, LZ, and PandaX-4T, enabling new constraints on DM-electron interactions after including Earth a...
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Ratio-Filter Dechirping converts gravitational-wave matched filtering from a memory-bound FFT into a cache-efficient FIR convolution, delivering a measured 8x speedup in the core loop.
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Cosmological long-wavelength solutions in non-adiabatic multi-fluid systems
Nonlinear long-wavelength solutions are constructed for cosmological perturbations in non-adiabatic multi-fluid systems, admitting adiabatic and entropy modes at leading order via ADM and gradient expansion.
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Strongly Interacting Dark Matter admixed Neutron Stars
Strongly interacting dark matter described by a first-principles G2 gauge-theory equation of state can be mixed into neutron stars while remaining compatible with current observational constraints.
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Boosting the optical depth to Thomson scattering with primordial black hole evaporation at high redshift
A monochromatic primordial black hole population can raise the CMB optical depth by at most Delta tau ~ 0.008 under current CMB data, leaving BAO-CMB tensions essentially unchanged.
-
Spectator Axions in String Inflation and Primordial Black Holes
In Fibre Inflation, spectator axions with f≲0.1 M_Pl leave the PBH power spectrum unchanged, while for f≳0.1 M_Pl and exponentially small non-perturbative prefactors they can raise P_R from 1.9e-4 to 3.5e-3 and enable...
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Assessing the Impact of Instrumental Requirements on the Scientific Performance of the Einstein Telescope
Degrading the Einstein Telescope's sensitivity in specific frequency bands hurts different science goals in predictable ways, but the mission remains scientifically strong even in the worst modelled cases.
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Primordial black holes forming during kination: the trapped, the overdense, and the void
In one non-attractor inflation model, initially similar field fluctuations produce three distinct black-hole formation channels—trapped, overdense, void—with collapse thresholds determined by the full density profile,...
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High-Energy Neutrinos from Black Hole Evaporation in Neutron Stars
Repeated collapse of asymmetric dark matter inside neutron stars into evaporating microscopic black holes can produce a Galactic-Center-concentrated high-energy neutrino flux at the 10^-12 GeV cm^-2 s^-1 level, subdom...
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High-Energy Neutrinos from Black Hole Evaporation in Neutron Stars
Dark matter collapsing inside neutron stars could repeatedly form microscopic black holes whose Hawking evaporation produces a detectable high-energy neutrino flux concentrated toward the Galactic Center.
-
Primordial Black Hole mass growth from neutrinos during the radiation era
PBHs of ~1e3–1e7 solar masses can significantly grow by absorbing neutrinos before matter-radiation equality.
-
The statistics of curvature-profile dispersion in primordial black hole formation
Shape dispersion around the average peak profile is a genuine statistical ingredient: rare deformed curvature profiles can dominate primordial black hole formation when the power spectrum is broad or non-Gaussianity i...
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Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity
Bumblebee gravity enhances primordial black hole abundance through three mechanisms, but the model harbors a ghost instability and a tachyonic instability that make it cosmologically unviable.
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Effect of post-recombination accretion on primordial binary black hole mergers within virialized dark matter halos
BHL-type post-recombination accretion can raise late three-body PBH merger rates enough for TianQin detections at f~10^{-6} and for LVK limits to bound delayed virialization.
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PBHs and GWs from Scaling Monopoles
Scaling monopoles generate PBHs via stochastic overdensities and GWs with correlated spectra, potentially with magnetically charged PBHs as a signature if the scaling ends via gauge boson mass.
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One Feature, Three Clocks: Phase-Locked Gravitational Waves, Primordial Black Holes, and Non-Gaussianity from Periodic Warm Inflation
Periodic warm inflation imprints one log-periodic feature on the curvature spectrum that saturates asteroid-mass PBHs, generates dual-band GW backgrounds, and offsets the bispectrum phase by a quarter cycle fixed by s...
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Memoirs of the curvaton: non-perturbative non-Gaussianity and supermassive primordial black holes
Curvaton self-interactions in non-quadratic potentials produce a local non-Gaussian map that enables supermassive primordial black hole formation at peak amplitudes of order 10^{-5} while remaining consistent with μ-d...
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String Axiverse Enhancement of Superradiant Dark Matter Production
O(100–10^5) light string axions enhance PBH spin-up during Hawking evaporation, boosting superradiant dark-matter cloud efficiency and expanding the micro-boson-star parameter space while contributing negligibly to ΔN_eff.
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Projecting the ultimate pulsar timing sensitivity to dark matter substructure in a stochastic gravitational wave background
Monte Carlo and ML surrogate framework projects PTA sensitivity to compact DM substructures and shows SGWB weakens it, with only Shapiro searches retaining sensitivity in optimistic cases.
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Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
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...
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The Gravitational Spectral Radio Forest: A Signature of Primordial Black Holes
Asteroid-mass primordial black holes induce a Riemann tidal splitting of the 2P_{3/2} hydrogen state, turning the 9.9 GHz line into a ~2 GHz bandwidth gravitational spectral radio forest in H II regions with accretion...
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Primordial Black Hole Hotspots Beyond Flat Spacetime
Hotspots around light primordial black holes cool faster in an expanding universe following T_plt ∝ t^{-11/15} and vanish completely in finite time, unlike everlasting hotspots in flat spacetime.
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Hig...
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High-energy neutrino constraints on primordial black holes as dark matter
High-energy neutrino telescopes constrain sub-asteroid mass primordial black holes with extended mass functions as dark matter, yielding limits slightly weaker than but independent of gamma-ray bounds.
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Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters
Monte Carlo solutions of the Smoluchowski equation for PBH clusters yield finite runaway timescales and evolving mass distributions that form high-redshift SMBHs, shortened further by mass segregation.
-
Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters
Monte Carlo solutions to the Smoluchowski coagulation equation yield runaway timescales and mass evolution for primordial black hole clusters at different redshifts based on cluster properties.
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Primordial black holes and the velocity acoustic oscillations features in 21 cm signals from the cosmic Dark Ages
Primordial black holes generate up to 30% amplitude VAO wiggles in 21 cm signals from the Dark Ages at redshifts 20-40 even at dark matter fractions as low as 10^-13.
-
STOchastic LAttice Simulation of hybrid inflation
In hybrid inflation, stochastic noise breaks topological defects into sub-Hubble-scale structures, and only the n=1 case leaves a global imprint on the curvature perturbation.
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Numerical simulations of primordial black hole formation via delayed first-order phase transitions
Spherically symmetric numerical relativity shows false-vacuum domains from delayed first-order phase transitions form type B (baby-universe) or type A (direct-collapse) primordial black holes, separated by a robust t_...
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Revisiting PBH accretion, evaporation and their cosmological consequences
Relativistic accretion onto Kerr primordial black holes gives roughly 4.5x mass growth and fast spin-down, strengthening BBN bounds, lowering the survival mass to ~2.7e14 g, and erasing the high-frequency stochastic g...
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In-depth analysis of the clustering of dark matter particles around primordial black holes. Part II. Analytical prescriptions for spikes
A 'soft' analytical approximation reproduces PBH minispike densities and annihilation rates to ~±15%, and shows that a discovered sub-solar PBH population would strongly constrain s-wave WIMP dark matter.
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Constraining memory-burdened primordial black holes with graviton-photon conversion and binary mergers
Derives gamma-ray upper limits on memory-burdened PBH dark matter abundance using graviton-photon conversion during recombination and merger-induced semiclassical evaporation, excluding mass windows 7.5e5-4.4e7 g and ...
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Atomic Quantum Sensors for High-Frequency Gravitational Wave Searches
A cavity-plus-atomic-sensor design could reach strain sensitivities down to ~1e-37 Hz^-1/2 in aggressive optical configurations, opening the unexplored high-frequency gravitational-wave band.
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GW231123: A Possible Primordial Black Hole Origin
GW231123's masses and high spins are consistent with primordial black holes that accreted mass and angular momentum in the early universe within the standard PBH framework.
-
Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order
Extends diagrammatic approach for scalar-induced gravitational waves to arbitrary-order local PNG, deriving semi-analytic spectra for energy density, anisotropies, bispectrum and trispectrum up to quartic terms.
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Scalar-induced gravitational waves from a box-shaped curvature power spectrum
Analytic SIGW spectra for a log-box curvature power spectrum: narrow-box geometric overlap factor turning IR slope k^{3}ln^{2}k into k^{2}ln^{2}k, plus broad-box product of universal edge functions.
-
Primordial Black Hole mass growth from neutrinos during the radiation era
Neutrino absorption lets intermediate-mass and supermassive primordial black holes grow during the radiation era, shifting thermal-history peaks and raising f_PBH.
-
Constraints on Primordial Black Hole Dressed by Dark Matter Halo from Microlensing Effect of Fast Radio Bursts
A new conversion formula turns monochromatic bare-PBH microlensing bounds into extended-mass dressed-PBH bounds, and a 10^5-FRB forecast places f_PBH near 10^-4.
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Constraining primordial non-Gaussianity and parity-violation through Scalar-Induced Gravitational Waves with next-generation ground-based interferometers
ET+CE forecast: injected SIGW parameters (A_p, f_peak, f_NL, tau_NL, parity-odd tau_tilde_NL) are recovered within 1-2 sigma despite an astrophysical foreground, but the chiral V-mode is sub-threshold (SNR 0.5-1.9).
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PBH formation and Gravitational Waves as Multi-messenger Signals of First-order Phase Transitions
False-vacuum collapse during first-order phase transitions can form PBHs and emit GWs across a broad parameter range, and MeV-scale classically conformal U(1)_{B-L} symmetry breaking has the largest region where both ...
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Cancellation of one-loop time dependence in superhorizon curvature perturbations from all scales
One-loop time dependence in superhorizon curvature perturbations cancels when all-scale contributions and boundary terms are included consistently via the δN formalism.
-
A Solar-System Window for Hidden Stellar Companions
The paper builds an illustrative mass-distance window for hidden-brane companions and finds overlap with the minimum mass of a QCD-scaled hidden star at the upper end of the allowed range.
-
String Axiverse Enhancement of Superradiant Dark Matter Production
O(100-10^5) string axions enhance PBH superradiance efficiency via increased spin, expanding viable mass-spin regions for micro-boson star dark matter while too many axions cause overly rapid evaporation.
-
Graviton Floor
Photon-to-graviton conversion in blazar jets dominates a new graviton background that sets a floor for high-frequency GW detectors, analogous to the neutrino floor.
-
Exciting the Vacuum: Non-Thermal Particle Bursts and Multi-Messenger Signals from Binary Black Holes
In the weak-field inspiral regime, binary black holes produce particles via a non-thermal power-law spectrum with dE/dt ∝ M^{10/3} ω^{16/3}.
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Universal Suppression of Gravitational Waves from Black Hole Evaporation Dynamics
Black hole populations with finite-width mass distributions exhibit universal late-time evaporation-driven evolution that produces characteristic power-law suppression of induced gravitational waves, directly linking ...
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This paper was first reviewed by grok-4.3 on May 15, 2026.
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