---
title: "How to read the 2026 primordial black hole review"
description: "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."
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language: "en"
page_type: "story"
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last_modified: "2026-11-12"
---

[Primordial black holes from early collapse to today’s limits](https://sandboxphysics.com/stories/primordial-black-holes/) L4 · Paper guide

# How to read the 2026 primordial black hole review

Sandbox Physics · 2026-11-12

Read arXiv:2601.06024v2 from Sec. VI and Figs. 4–6 outwards. Fig. 4 compiles single-mass limits; Sec. VI explains why a mass function cannot be read off it. Then Sec. II.A.2 shows how non-Gaussian statistics move the abundance, Secs. III and IV.E cover evaporation and accretion, Sec. IV.C the gravitational-wave limits and Sec. V the asteroid-mass window. Keep four labels apart while reading: measured limits, the review’s own synthesis, model results and open claims.

## Before you begin

The L1–L3 chapters of this series. The guide is for readers who will open the paper alongside it.

## Which version, and where to start

This guide uses version 2 on arXiv, dated 1 April 2026, by Carr, Iovino, Perna, Vaskonen and Veermäe. arXiv lists the journal reference Riv. Nuovo Cim. (2026); the guide was checked against the arXiv text, not the journal typesetting, so equation or figure numbers may differ there.

Start with the caption of Fig. 4. It compiles limits for a monochromatic population: every black hole at one mass. Bold curves are limits; dashed curves mark potential evidence, labelled SNe, OGLE and LVK in the caption. The figure maps what each probe excludes at a single mass; testing a formation model takes the integral of Sec. VI.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026)

## Sec. VI and Figs. 5–6: extended mass functions

Sec. VI gives the rule for linear probes in Eqs. 25–28 and the quadrature combination in Eq. 29, the same relations derived in the L3 chapter from Carr et al. 2017. Read the paragraph on limitations next to them: mergers, Poisson clustering, Lyman-alpha, dynamical limits, mass segregation and accretion each make the rule approximate or inapplicable, and the authors suggest treating the result as an effective mass function.

Fig. 5 has four panels: a critical-collapse mass function, a lognormal with $\sigma=1$ and two cut power laws with opposite slopes. Solid curves are the extended-mass-function limits and dashed curves the monochromatic ones. The text refers to the colour-coded map of the lognormal width against the mean mass as the “right panel of Fig. 5”; in v2 that map is the left panel of Fig. 6. The review states that the asteroid-mass window closes for widths above about $\sigma\approx2.5$.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026) · Carr, Raidal, Tenkanen, Vaskonen & Veermäe · Primordial black hole constraints for extended mass functions · arXiv:1705.05567v3, Phys. Rev. D 96, 023514 (2017)

## Sec. II.A.2: non-Gaussian tails

The abundance comes from a far tail, so anything that changes the tail changes the answer by orders of magnitude. The review separates two channels. The relation between curvature and density is non-linear, which matters even when the curvature perturbation is Gaussian. The curvature perturbation itself can also be non-Gaussian, as in curvaton or ultra-slow-roll models.

The local expansion of Eq. 16, with coefficients $f_{\rm NL}$ and $g_{\rm NL}$, is the familiar starting point, but the review notes that it fails for the closed forms of the curvaton and ultra-slow-roll cases. A truncated series can converge for a narrow spectrum; a broad spectrum needs a non-perturbative treatment.

Fig. 2 shows a mass function near one solar mass changing with the curvaton decay parameter $r_{\rm dec}$. Fig. 3 shows the spectrum amplitude needed for $f=1$, with a threshold of 0.55, for the curvaton and an ultra-slow-roll-like case. Keeping only the quadratic term overestimates the abundance for the curvaton and underestimates it for the ultra-slow-roll-like case. These are model calculations: they show how large the effect can be, not which model is realised.

$$
\zeta=\zeta_{\rm G}+\frac35f_{\rm NL}\,\zeta_{\rm G}^2+\frac{9}{25}g_{\rm NL}\,\zeta_{\rm G}^3+\dots
$$

The review’s Eq. 16. The Lab sets every non-Gaussian term to zero.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026)

## Secs. III and IV.E: evaporation and accretion

Sec. III gives the Hawking temperature (Eq. 21) and the lifetime (Eq. 23), about $0.4\,\mathrm{s}\,(M/10^{9}\,\mathrm{g})^3$. A non-rotating black hole born with about $5\times10^{14}$ grams is finishing its evaporation today. Lighter ones are gone and constrained through their effect on nucleosynthesis and the photon backgrounds, the limits summarised by Carr et al. 2010.

Sec. IV.E covers black holes heavier than about ten solar masses, whose accretion would heat gas and change recombination, the CMB, X-ray counts and the 21-cm signal. The review stresses that these limits depend on the accretion model, such as disk versus spherical inflow and the Bondi rate. Accretion can also grow the black holes and weaken limits, while clustering can strengthen them. Serpico et al. 2020 is one such CMB analysis; its abstract says the result depends on accretion physics.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026) · Carr, Kohri, Sendouda & Yokoyama · New cosmological constraints on primordial black holes · arXiv:0912.5297v2, Phys. Rev. D 81, 104019 (2010) · 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)

## Sec. IV.C: gravitational waves

Black holes that pair up in the early universe would merge today. With hundreds of LIGO-Virgo-KAGRA mergers now observed, the review quotes a merger limit of about $f\lesssim0.1\%$ from an O3 analysis; the abstract of Andrés-Carcasona et al. 2024 gives the same order, about $10^{-3}$ between 1 and 200 solar masses, for several mass functions. The stochastic background gives a weaker limit of order $10^{-2}$. Limits from scalar-induced gravitational waves are discussed separately and are not drawn in Fig. 4.

The same section lists potential evidence: events in the mass gaps at about 60–120 and 2–5 solar masses, and a sub-solar-mass candidate from the GstLAL search with a false-alarm rate of one in five years. The review reports them as possibilities; this guide relies on the review’s account of them.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026) · 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)

## Sec. V: the asteroid-mass window

Between about $10^{-17}$ and $10^{-10}$ solar masses, black holes could still be all of the dark matter. The review explains why several proposed limits there no longer hold: hydrodynamic simulations removed the white-dwarf ignition limit, femtolensing limits are invalid, limits from neutron stars in globular clusters are uncertain, and main-sequence lifetimes are unaffected.

Its upper edge is set by microlensing. The Subaru limit is weaker than first published once finite source size is included, as the Smyth et al. 2020 abstract states. Future tests the review names include X-ray microlensing with instruments such as NICER and STROBE-X, reaching below about $10^{-13}$ solar masses, and solar-system ephemerides.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026) · 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) · Particle Data Group · Review 27, Dark Matter (2025 edition, 1 December 2025)

## Sorting the claims

Published limits from data: OGLE microlensing (Mróz et al., Nature 2024), the revised Subaru limit (Smyth et al. 2020), the O3 merger analysis (Andrés-Carcasona et al. 2024) and the CMB accretion limit (Serpico et al. 2020). This series read their abstracts only, so it relies on their stated results, not on a check of their methods.

The review’s synthesis: the Fig. 4 compilation, the extended-mass-function treatment in Sec. VI and the judgement about which old limits are invalid. The guide read these sections in full in arXiv v2.

Model results: the non-Gaussian amplitudes of Figs. 2–3, the accretion-model dependence and the Lab’s own Gaussian, linear formation model. They show how a prediction responds to an assumption.

Open claims: the mass-gap and sub-solar candidates, the correlation in source-subtracted infrared and X-ray backgrounds named in Sec. IV.E, and whether black holes make up any of the dark matter at all. Primordial black holes remain candidates; no population has been confirmed.

Reading: Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026) · Mróz, Udalski et al. · No massive black holes in the Milky Way halo · arXiv:2403.02386v3, Nature 632, 749 (2024) · 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) · 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) · 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)

## [Find the review’s figures in the Lab](https://sandboxphysics.com/labs/primordial-black-hole-mass-function/)

1. The default preset puts all the dark matter in the asteroid-mass window. Check that the tightest ratio, Subaru at about 0.08, stays far below one.
2. Choose “Ruled out by evaporation” and read the evaporation ratio of about 50; locate the matching part of Fig. 4.
3. Choose “Stellar-mass black holes”. The gravitational-wave ratio is greyed out; explain why, using Sec. VI and Sec. IV.C.

## Exercises with explanations

1. A talk shows a lognormal mass function drawn on top of Fig. 4 and says it is allowed because it never crosses a curve. What two questions should you ask?

   Read the explanation

   First, was it tested with the integral of Sec. VI, Eqs. 25–28, rather than by eye? A density per $\ln M$ cannot be compared with a curve that caps a total. Second, are the probes in the relevant mass range linear in $\psi$? If the decisive limit is a merger rate, the linear rule does not apply and the answer needs the merger analysis itself.

2. Why does the review say the asteroid window closes for widths above about 2.5, when the monochromatic curves leave it open?

   Read the explanation

   A wide lognormal centred in the window puts part of its mass below about $10^{-17}$ solar masses, where evaporation limits are strong, and part above $10^{-10}$, where microlensing is strong. The weighted ratio adds those contributions, so a spread that is safe at its centre can fail through its tails.

3. Fig. 3 uses a threshold of 0.55, while the Lab defaults to 0.45. Can you compare its amplitudes with the Lab’s?

   Read the explanation

   Not directly. The required amplitude depends steeply on the threshold, the window function and the definition of the density contrast. Compare trends within one paper’s conventions, such as how the curvaton and ultra-slow-roll cases depart from the quadratic approximation.

[Previous: Extend a microlensing limit to a spread of black hole masses](https://sandboxphysics.com/stories/primordial-black-holes/extend-a-microlensing-limit-to-a-mass-spread/)

## Sources and how much of each was read

1. [Carr, Iovino, Perna, Vaskonen & Veermäe · Primordial black holes: constraints, potential evidence and prospects · arXiv:2601.06024v2 (1 April 2026)](https://arxiv.org/abs/2601.06024v2)

   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.

2. [Carr, Raidal, Tenkanen, Vaskonen & Veermäe · Primordial black hole constraints for extended mass functions · arXiv:1705.05567v3, Phys. Rev. D 96, 023514 (2017)](https://arxiv.org/abs/1705.05567v3)

   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.

3. [Particle Data Group · Review 27, Dark Matter (2025 edition, 1 December 2025)](https://pdg.lbl.gov/2025/reviews/rpp2025-rev-dark-matter.pdf)

   Sections 27.1, 27.3 and 27.7: formation time and mass, the main classes of limits and the window of roughly $10^{17}$ to $10^{21}$ grams.

4. [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)](https://arxiv.org/abs/1910.01285v2)

   Abstract only. Larger source stars in M31 weaken the Subaru HSC microlensing limit by up to almost three orders of magnitude in some cases.

5. [Mróz, Udalski et al. · No massive black holes in the Milky Way halo · arXiv:2403.02386v3, Nature 632, 749 (2024)](https://arxiv.org/abs/2403.02386v3)

   Abstract only. Twenty years of OGLE data on nearly 80 million LMC stars: no events longer than one year, so compact objects from $1.8\times10^{-4}$ to 6.3 solar masses make up at most 1% of the dark matter.

6. [Carr, Kohri, Sendouda & Yokoyama · New cosmological constraints on primordial black holes · arXiv:0912.5297v2, Phys. Rev. D 81, 104019 (2010)](https://arxiv.org/abs/0912.5297v2)

   Abstract only. Limits from evaporation on nucleosynthesis and the extragalactic photon background for $10^{9}$ to $10^{17}$ grams.

7. [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)](https://arxiv.org/abs/2002.10771v2)

   Abstract only. Accretion changes the ionization history seen in the CMB; the bound reaches a fraction of $3\times10^{-9}$ near $10^{4}$ solar masses and depends on accretion physics.

8. [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)](https://arxiv.org/abs/2405.05732v2)

   Abstract only. A hierarchical analysis of O3 mergers with several mass functions limits PBHs to at most about $10^{-3}$ of the dark matter between 1 and 200 solar masses.

## Keep reading

Black holes from the first second · Reading path

### Black holes from the first second

1. [Article **How to look for black holes that formed before the first stars**](https://sandboxphysics.com/stories/primordial-black-holes/how-to-find-black-holes-older-than-stars/)
2. [Article **When a dense patch of the early universe becomes a black hole**](https://sandboxphysics.com/stories/primordial-black-holes/how-an-early-overdensity-becomes-a-black-hole/)
3. [Article **How a rare Gaussian tail sets the number of primordial black holes**](https://sandboxphysics.com/stories/primordial-black-holes/how-a-rare-gaussian-tail-sets-the-abundance/)
4. [Article **Testing a spread of black hole masses against many observations**](https://sandboxphysics.com/stories/primordial-black-holes/test-a-mass-spread-against-many-limits/)
5. [Article **Extend a microlensing limit to a spread of black hole masses**](https://sandboxphysics.com/stories/primordial-black-holes/extend-a-microlensing-limit-to-a-mass-spread/)
6. [You are here **How to read the 2026 primordial black hole review**](https://sandboxphysics.com/stories/primordial-black-holes/read-the-2026-primordial-black-hole-review/)