Primordial black holes from early collapse to today’s limits
If black holes formed in the first second, before any star, they would still be here, and their total mass could be some or all of the dark matter. Finding them means predicting a mass function from the early universe and testing it against lensing, evaporation, accretion and gravitational-wave limits.
How to look for black holes that formed before the first stars
Look for what their mass and radiation would do today: evaporation, brightened starlight, heated gas and mergers. One mass range is still open.
L1When a dense patch of the early universe becomes a black hole
Derive the horizon mass in the radiation era, the collapse threshold and the black hole mass, then follow two worked examples from asteroid to stellar mass.
L2How a rare Gaussian tail sets the number of primordial black holes
Go from a curvature spectrum to the density variance, the collapsed fraction and today’s mass function, and see why a 15% change matters.
L3Testing a spread of black hole masses against many observations
Derive the weighted ratio for one linear observation, combine several only under stated assumptions and see why overlaying limit curves fails.
TutorialExtend a microlensing limit to a spread of black hole masses
A standard-library Python script turns one published single-mass limit into a limit on a lognormal spread, with saved inputs, outputs, errors and refusals.
L4 · Paper guideHow to read the 2026 primordial black hole review
A section-by-section guide to Carr et al. 2026 (arXiv v2): which figure to open first, which claims are limits, which are model results and which remain open.
A short explainer comes first. Three course chapters derive the horizon mass, the abundance from a rare Gaussian tail and the rule for testing a mass function. A Python tutorial extends one microlensing limit to a spread of masses, and the last guide reads the 2026 review section by section.
Sources and how much of each was read
- Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026)
Review; arXiv lists the journal reference Riv. Nuovo Cim. (2026). Read in full: Sec. II.A.2 on non-Gaussianity, Sec. IV.C (gravitational waves), IV.E (accretion), V (asteroid-mass window), VI (Eqs. 25–29) and the captions of Figs. 2–6; parts of Sec. II and III.
- Carr, Raidal, Tenkanen, Vaskonen & Veermäe · Primordial black hole constraints for extended mass functions · arXiv:1705.05567v3, Phys. Rev. D 96, 023514 (2017)
Full text. The linear rule for one observable (Eq. 12) and the quadrature combination of several (Eq. 13), with the assumptions under which they hold.
- Young, Byrnes & Sasaki · Calculating the mass fraction of primordial black holes · arXiv:1405.7023v4, JCAP 1407 (2014) 045
Sections 1–4.2: the smoothed density variance with a Gaussian window, the Press–Schechter tail and the printed bound of Eq. 28 used as an independent check.
- Sasaki, Suyama, Tanaka & Yokoyama · Primordial black holes: perspectives in gravitational wave astronomy · arXiv:1801.05235v1
Section 2.3, Eqs. 21–31: horizon mass, collapse efficiency and the present abundance per formation fraction.
- Harada, Yoo & Kohri · Threshold of primordial black hole formation · arXiv:1309.4201v4, Phys. Rev. D 88, 084051 (2013)
Abstract only. For radiation it gives a threshold amplitude of about 0.41 in the measure used by numerical simulations.
- Particle Data Group · Review 27, Dark Matter (2025 edition, 1 December 2025)
Sections 27.1, 27.3 and 27.7: formation time and mass, the main classes of limits and the window of roughly to grams.
- Vaskonen · PBHconstraints digitized limits, commit ef2fb03 (MIT license)
Five tables used unchanged: EGR, SUB, OGLE, acc and LIGO, with SHA-256 hashes recorded. The table-to-paper mapping follows the repository notebook.
- Smyth, Profumo, English, Jeltema et al. · Updated constraints on asteroid-mass primordial black holes as dark matter · arXiv:1910.01285v2, Phys. Rev. D 101, 063005 (2020)
Abstract only. Larger source stars in M31 weaken the Subaru HSC microlensing limit by up to almost three orders of magnitude in some cases.
- Mróz, Udalski et al. · No massive black holes in the Milky Way halo · arXiv:2403.02386v3, Nature 632, 749 (2024)
Abstract only. Twenty years of OGLE data on nearly 80 million LMC stars: no events longer than one year, so compact objects from to 6.3 solar masses make up at most 1% of the dark matter.
- Carr, Kohri, Sendouda & Yokoyama · New cosmological constraints on primordial black holes · arXiv:0912.5297v2, Phys. Rev. D 81, 104019 (2010)
Abstract only. Limits from evaporation on nucleosynthesis and the extragalactic photon background for to grams.
- Serpico, Poulin, Inman & Kohri · Cosmic microwave background bounds on primordial black holes including dark matter halo accretion · arXiv:2002.10771v2, Phys. Rev. Research 2, 023204 (2020)
Abstract only. Accretion changes the ionization history seen in the CMB; the bound reaches a fraction of near solar masses and depends on accretion physics.
- Andrés-Carcasona, Iovino, Vaskonen & Veermäe · Constraints on primordial black holes from LIGO-Virgo-KAGRA O3 events · arXiv:2405.05732v2, Phys. Rev. D 110, 023040 (2024)
Abstract only. A hierarchical analysis of O3 mergers with several mass functions limits PBHs to at most about of the dark matter between 1 and 200 solar masses.