Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts

Amanda Weltman; Shruti Bhatporia; Surajit Kalita

REVIEW 3 major objections 3 minor 11 references

FRB lensing bounds on primordial black holes are gravity-model-dependent: a modified-gravity term shifts the constraints and mimics plasma scattering.

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 →

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T0 review

2026-08-03 00:35 UTC pith:7WOTGP3Q

load-bearing objection Kappa scan of PBH constraints recycles GR optical depth with a modified time delay, so the claimed gravity-model dependence and plasma-lensing mimicry aren't established yet. the 3 major comments →

arxiv 2607.28704 v1 pith:7WOTGP3Q submitted 2026-07-30 astro-ph.CO astro-ph.HEgr-qc

Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts

Surajit Kalita , Shruti Bhatporia , Amanda Weltman This is my paper

classification astro-ph.CO astro-ph.HEgr-qc

keywords fast radio burstsprimordial black holesdark mattermodified gravitygravitational lensingCHIMEplasma lensingtime delay

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether fast radio bursts (FRBs) can still pin down how much dark matter is made of primordial black holes if gravity differs from general relativity. Using 636 CHIME bursts, the authors show that the upper limit on the primordial-black-hole fraction shifts substantially as a modified-gravity parameter κ is varied. They also find that the lensing time-delay signature of this modified gravity resembles the scattering screen produced by plasma, rather than standard gravitational lensing. The consequence is that FRB-based constraints on dark-matter black holes are gravity-model-dependent, and a future lensed FRB could be misread as plasma physics when it is actually a sign of modified gravity.

Core claim

The paper's central claim is that in a scalar-tensor modified-gravity framework whose point-mass metric is Schwarzschild–de Sitter-like with an added κr² term, the differential time delay between two lensed FRB images acquires an extra term proportional to (1/c√κ) tan⁻¹(...). This extra term changes the optical depth for lensing and, through Poisson statistics on zero confirmed lensed FRBs, yields an upper bound on fPBH that varies strongly with κ (Fig. 1). The same κ term produces a cutoff in the minimum detectable time delay that reproduces the behavior of a plasma scattering screen, meaning modified gravity can mimic plasma lensing in FRB observations.

What carries the argument

The central object is the modified metric ds² = (1 - 2GM_L/c²r + κr²)c²dt² - (1 - 2GM_L/c²r + κr²)⁻¹dr² - r²(dθ² + sin²θ dϕ²), with the claim that this is a solution for a general scalar-tensor gravity framework. The argument is carried by the time-delay formula Eq. (2.2), whose inverse-tangent term depends on κ; this term is what shifts the fPBH exclusion curves and what creates the plasma-scattering-like cutoff in the time-delay distribution.

Load-bearing premise

The load-bearing premise is that the metric in Eq. (2.1) really is the general vacuum solution for a broad class of scalar-tensor gravity theories; if the κr² term is only a cosmological-constant-like special case, the κ-dependent bounds and the plasma-mimicry conclusion apply only to that special case, not to modified gravity in general.

What would settle it

Find a physically viable scalar-tensor theory whose static, spherically symmetric vacuum solution provably differs from Eq. (2.1) — for example by containing a logarithmic or r⁻ⁿ term — and the paper's claim that Eq. (2.1) represents a general scalar-tensor framework collapses. Observationally, detect one lensed FRB and measure the inter-image time delay at two or more radio frequencies: a plasma screen produces a ν⁻² delay, while the modified-gravity geometric delay is achromatic, so a frequency-independent delay would rule out the plasma-lensing interpretation.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

The fPBH upper limit derived from CHIME FRBs is not a single number: it shifts by orders of magnitude as κ ranges from 10⁻³⁰ to 10⁻²⁰ cm⁻².
A null search for lensed FRBs cannot be translated into a unique constraint on dark-matter black holes unless the gravity model is specified.
The κ-induced cutoff in the time-delay distribution mimics a plasma scattering screen, so a lensed FRB with such a cutoff could be misinterpreted as plasma lensing rather than modified gravity.
CHIME's minimum detectable time delay of roughly 10⁻⁹ s sets the left-hand cutoff of each exclusion curve, while the magnification threshold sets the right-hand cutoff.
Future radio telescopes with higher sensitivity, such as HIRAX, SKA, CHORD, DSA-2000, and BURSTT, should sharpen these constraints and may distinguish the modified-gravity signature.

Where Pith is reading between the lines

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

Not stated by the paper: the degeneracy between modified gravity and plasma lensing means that any future lensed-FRB candidate with an apparent time-delay cutoff must be followed up at multiple radio frequencies — plasma delays scale with frequency while the geometric modified-gravity delay does not.
Not stated by the paper: the same data could be consistent with fPBH near zero in general relativity but with a much larger fPBH in modified gravity, so the 'dark matter made of black holes' question is entangled with the choice of gravitational theory.
Not stated by the paper: if a lensed FRB with a measured time delay is ever confirmed, fitting the tan⁻¹ form of Eq. (2.2) would directly constrain κ, turning the current degeneracy into a probe of modified gravity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Kappa scan of PBH constraints recycles GR optical depth with a modified time delay, so the claimed gravity-model dependence and plasma-lensing mimicry aren't established yet.

read the letter

Colleague,

This is a condensed IAU proceedings piece, not a full paper. The genuinely new content is Fig. 1: a scan of their earlier time-delay formula over the modified-gravity parameter κ, applied to 636 CHIME FRBs, plus a qualitative remark that the resulting cutoff mimics plasma scattering. That's a reasonable thing to plot, and the intended message — that FRB lensing constraints on PBH dark matter may be gravity-model dependent — is worth taking seriously.

I have to flag a load-bearing problem, and here I agree with the stress-test note. The optical depth in Eq. (2.5) comes from Muñoz et al. (2016) and that derivation assumes the Schwarzschild Einstein radius θ_E. The time delay in Eq. (2.2) comes from the metric (2.1), which includes κ r². For this metric, the deflection angle and the Einstein radius should acquire κ corrections, and those corrections change the cross-section in τ. The paper quotes the GR formula verbatim and does not derive a modified version. So the κ-dependent shifts in Fig. 1 could be an artifact of combining a GR geometric factor with a modified propagation delay. That is central, because the 'mimics plasma lensing' claim rests on the κ-induced cutoff in y_min.

There are smaller issues. The source redshifts come from the Macquart relation with fixed DM_Halo=50 pc cm^-3 and DM_Host=117 pc cm^-3 and no scatter, so Fig. 1 has no uncertainty band. That is minor for a proceedings, but it does mean the absolute f_PBH bounds are approximate. The statement that (2.1) is 'a solution for a general scalar-tensor gravity theory framework' is asserted without references or derivation; that is load-bearing if the constraints are to be read as generic modified gravity rather than one particular theory.

Credit where due: the authors are transparent about what comes from their earlier work and from Muñoz et al.; the Poisson bound is a genuine zero-event upper limit, no quantity is fitted to hit a f_PBH target. The qualitative overlap with the Leung et al. plasma-lensing cutoff is a useful hint, even if it is only curve similarity.

Who is this for? Someone tracking FRB lensing or PBH dark matter. It's a four-page pointer to an open problem, not the last word. I would not cite it for constraints, but I might cite it as a flag that the modified-gravity case needs a proper treatment.

Recommendation: send to peer review rather than desk-reject, but any referee should require a derivation of the modified Einstein radius and optical depth, or the authors should reframe the paper as a preliminary note. As it stands, the headline claim is plausible but not established.

Referee Report

3 major / 3 minor

Summary. The paper uses 636 CHIME/FRB events to constrain the fraction f_PBH of dark matter in primordial black holes within a modified-gravity framework based on the de Sitter–Schwarzschild metric of Eq. (2.1). Source redshifts are inferred from the Macquart mean DM_IGM relation with fixed DM_Halo ≈ 50 pc cm⁻³ and DM_Host = 117 pc cm⁻³. The lensing optical depth is taken from Muñoz et al. (2016), the modified-gravity time delay from Kalita et al. (2023), and a Poisson zero-detection upper limit yields the f_PBH exclusion curves in Fig. 1, which shift with the modified-gravity parameter κ. The paper further claims that modified gravity introduces a screening effect mimicking plasma lensing (Abstract, Sec. 3).

Significance. If the central derivation is sound, the paper would demonstrate that FRB lensing constraints on PBH dark matter depend nontrivially on the gravitational theory and that a modified-gravity screening effect could be mistaken for plasma scattering. This is potentially interesting for interpreting current and future FRB lensing searches. The paper also connects to a growing literature using FRBs as cosmological and fundamental-physics probes. However, the significance is tempered by the proceedings format: the central equations (2.2) and (2.5) are imported from prior work, and the uniqueness of the modified-gravity prediction is not established independently. The paper does not provide machine-checkable code or a full derivation of the modified-gravity lensing quantities, so its contribution rests on prior results that are not reproduced here.

major comments (3)

[Sec. 2, Eq. (2.1)] The metric (2.1) is asserted to be 'a solution for a general scalar-tensor gravity theory framework.' This is a load-bearing claim because the abstract and conclusions generalize the results to modified gravity broadly. The de Sitter–Schwarzschild form with a κr² term is a specific parametrization, not a generic scalar-tensor solution. The paper should either provide a derivation or a precise citation showing that Eq. (2.1) represents a general scalar-tensor framework, or restrict the claims to the particular theory that admits this metric. Without this, the statement that 'modified gravity mimics plasma lensing' is overgeneralized.
[Eqs. (2.2), (2.5) and Fig. 1] The central numerical result couples the standard GR optical depth formula (2.5) — which assumes the Schwarzschild Einstein radius and lensing cross-section of Muñoz et al. (2016) — with the modified-gravity time delay (2.2). For the metric (2.1), the null geodesics, deflection angle, and Einstein radius receive κ-dependent corrections. The paper does not derive a modified θ_E or a modified lensing cross-section; it uses the GR formula verbatim. The κ-dependent shifts in Fig. 1 may therefore be an artifact of combining a GR geometric factor with a modified time delay rather than a genuine prediction. The claim that FRB lensing constraints are gravity-model-dependent requires a self-consistent computation of the modified-gravity lensing optical depth.
[Sec. 2, Eqs. (2.3)–(2.6)] The numerical constraints are computed using fixed values DM_Halo ≈ 50 pc cm⁻³ and ⟨DM_Host⟩ = 117 pc cm⁻³ and the mean Macquart relation (2.4) with no scatter. Real FRB sightlines have significant variance in these quantities, which propagates into the inferred z_S and hence into the optical depth τ(M_L, z_S). Fig. 1 shows no uncertainty band or systematic-error assessment, so the exclusion curves are presented with an unjustified precision. A robustness check varying DM_Halo and DM_Host within plausible ranges is needed to support the quantitative constraints.

minor comments (3)

[Title/Abstract] The phrase 'primordial mass black holes' should be 'primordial black holes' for consistency with standard terminology.
[Header] The header contains both '32nd IAU General Assembly' and 'XXIXth IAU General Assembly, August 2015,' which is inconsistent. The date and assembly number should be corrected.
[Fig. 1] The figure legend lists κ values in units of cm⁻², but the text does not state whether these are comoving or physical units, nor what ranges are astrophysically motivated. Adding a brief explanation would help the reader interpret the curves.

Circularity Check

0 steps flagged

No significant circularity: the fPBH constraint is a genuine Poisson upper limit; self-cited equations are model inputs, not fitted predictions.

full rationale

The derivation chain is: adopt the modified metric (2.1); use the time delay (2.2) from Kalita et al. (2023) to set y_min; compute the optical depth (2.5) from Muñoz et al. (2016); average over the CHIME sample (2.6); and convert the absence of confirmed lensed FRBs into the Poisson upper limit (2.7). No quantity in this chain is fitted to the target fPBH; κ is an input parameter, and the zero-lensed-FRB count is an external observational input. Equation (2.7), although cited from Kalita et al. (2023), is a standard Poisson zero-event bound; substituting τ1 = \barτ/fPBH gives \barτ < ln(N/(N-1)), i.e., fPBH τ1 < ln(N/(N-1)), so the inequality is not an identity or a rearrangement of the assumed fPBH dependence. The main self-citation is that the modified-gravity time delay (2.2) is taken from the authors' prior work without re-derivation, but applying a previously derived formula is reliance on prior results rather than a circular fit. A possible physical inconsistency—using the GR optical depth (2.5) with the modified time delay (2.2) without a modified Einstein radius—would be a correctness or modeling concern, not a circularity. Therefore no circular step is identified; at most there is minor self-citation, giving score 2.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

No new particle, force, or conserved quantity is introduced; κ is a metric parameter rather than an invented entity. The main unverified inputs are the fixed DM components and the arbitrary κ values, plus the unsupported identification of Eq. (2.1) with generic modified gravity.

free parameters (5)

κ (modified gravity parameter) = 0, 10⁻³⁰, 10⁻²⁵, 10⁻²⁰ cm⁻² (plotted)
Introduced via the κr² term in Eq. (2.1); no mapping to a specific modified-gravity theory or observational prior is given, and the fPBH curves are evaluated at these chosen values.
DMHost (host galaxy dispersion) = 117 pc cm⁻³ (fixed mean)
Chosen as a constant for every FRB in Eq. (2.3); real host DM scatter is large and this affects the derived zS and hence the optical depth.
DMHalo (Galactic halo dispersion) = ≈ 50 pc cm⁻³
Fixed value subtracted from every FRB DM in Eq. (2.3); no uncertainty is propagated.
Minimum time-delay cutoff Δt_min = 10⁻⁹ s
Used as the left-hand cutoff in Fig. 1, attributed to CHIME resolution via Leung et al. (2022); this instrument threshold sets the low-mass boundary of the constraints.
Magnification cutoff μ_max = 1 < μ < S/N/3
Used for the right-hand cutoff in Fig. 1; the text does not specify how S/N is evaluated or how μ maps to y_max in Eq. (2.5).

axioms (5)

ad hoc to paper The de Sitter–Schwarzschild metric Eq. (2.1) represents a generic scalar-tensor modified-gravity theory.
Asserted in Sec. 2 without derivation or citation; the κr² term is more naturally a cosmological-constant-like term, not a proven general scalar-tensor solution.
domain assumption No FRB in the CHIME sample is confirmed to be lensed.
This is required to turn the Poisson zero-detection probability into Eq. (2.7); it depends on the current classification of the 636 bursts.
domain assumption The Macquart mean relation (Eq. 2.4) gives DMIGM for each individual FRB.
Used to solve Eq. (2.3) for zS for every burst; individual line-of-sight scatter around the mean is ignored.
domain assumption Standard ΛCDM cosmology with the given H(z) is assumed when computing angular diameter distances and DMIGM.
The constraints are explicitly framed 'within the standard ΛCDM cosmological framework' (Sec. 2), so modified gravity is only present in the lensing metric, not in the background cosmology.
standard math Poisson statistics with zero observed lensed events correctly describe the lensing count.
Eq. (2.7) uses the Poisson probability that no event occurs; this is valid if lensing events are independent and detection efficiency is uniform.

reviewed 2026-08-03 · how reviews work

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Cite this review

Pith. "Pith review of Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts." pith.science (2026). https://pith.science/paper/7WOTGP3Q

@misc{pith2026260728704,
  author       = {Pith},
  title        = {Pith review of: Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WOTGP3Q}},
  note         = {Machine review of arXiv:2607.28704}
}

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read the original abstract

In recent decades, a multitude of modified gravity theories have been proposed to address a variety of cosmological and astrophysical problems. While many of these theories remain viable, observational constraints on their parameters are increasingly stringent. Fast Radio Bursts (FRBs), in particular, have emerged as powerful probes of cosmology and fundamental physics. This study investigates the implications of a generic modified gravity theory for gravitational lensing by FRBs. By analyzing the dataset of CHIME/FRBs, we constrain the fraction of dark matter composed of primordial black holes within this theoretical framework. Furthermore, we demonstrate that modified gravity introduces a screening effect on gravitational lensing, analogous to the scattering effect of plasma on light rays.

Figures

Figures reproduced from arXiv: 2607.28704 by Amanda Weltman, Shruti Bhatporia, Surajit Kalita.

discussion (0)

Reference graph

Works this paper leans on

11 extracted references · 11 linked inside Pith

[1]

, keywords =

Continuous gravitational wave detection to understand the generation mechanism of fast radio bursts. , keywords =. doi:10.1093/mnras/stad392 , archivePrefix =. 2211.00940 , primaryClass =

Pith/arXiv arXiv
[2]

JCAP , keywords =

Gravitational lensing in modified gravity: a case study for Fast Radio Bursts. JCAP , keywords =. doi:10.1088/1475-7516/2023/11/059 , archivePrefix =. 2308.16604 , primaryClass =

Pith/arXiv arXiv 2023
[3]

Nature , keywords =

A census of baryons in the Universe from localized fast radio bursts. Nature , keywords =. doi:10.1038/s41586-020-2300-2 , archivePrefix =. 2005.13161 , primaryClass =

Pith/arXiv arXiv 2005
[4]

PRL , keywords =

Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter. PRL , keywords =. doi:10.1103/PhysRevLett.117.091301 , archivePrefix =. 1605.00008 , primaryClass =

Pith/arXiv arXiv
[5]

PRD , keywords =

Constraining primordial black holes using fast radio burst gravitational-lens interferometry with CHIME/FRB. PRD , keywords =. doi:10.1103/PhysRevD.106.043017 , archivePrefix =. 2204.06001 , primaryClass =

Pith/arXiv arXiv
[6]

, keywords =

The Fast Radio Burst-emitting Magnetar SGR 1935+2154-Proper Motion and Variability from Long-term Hubble Space Telescope Monitoring. , keywords =. doi:10.3847/1538-4357/ac432f , archivePrefix =. 2112.07023 , primaryClass =

Pith/arXiv arXiv 1935
[7]

, keywords =

A living theory catalogue for fast radio bursts. , keywords =. doi:10.1016/j.physrep.2019.06.003 , archivePrefix =. 1810.05836 , primaryClass =

Pith/arXiv arXiv 2019
[8]

, keywords =

The First CHIME/FRB Fast Radio Burst Catalog. , keywords =. doi:10.3847/1538-4365/ac33ab , archivePrefix =. 2106.04352 , primaryClass =

Pith/arXiv arXiv
[9]

, keywords =

A fast radio burst associated with a Galactic magnetar. , keywords =. doi:10.1038/s41586-020-2872-x , archivePrefix =. 2005.10828 , primaryClass =

Pith/arXiv arXiv 2005
[10]

, keywords =

A bright millisecond-duration radio burst from a Galactic magnetar. , keywords =. doi:10.1038/s41586-020-2863-y , archivePrefix =. 2005.10324 , primaryClass =

Pith/arXiv arXiv 2005
[11]

, keywords =

First Constraints on Compact Dark Matter from Fast Radio Burst Microstructure. , keywords =. doi:10.3847/1538-4357/aba7bb , archivePrefix =. 2002.12533 , primaryClass =

Pith/arXiv arXiv 2002

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.

[1] [1]

, keywords =

Continuous gravitational wave detection to understand the generation mechanism of fast radio bursts. , keywords =. doi:10.1093/mnras/stad392 , archivePrefix =. 2211.00940 , primaryClass =

Pith/arXiv arXiv

[2] [2]

JCAP , keywords =

Gravitational lensing in modified gravity: a case study for Fast Radio Bursts. JCAP , keywords =. doi:10.1088/1475-7516/2023/11/059 , archivePrefix =. 2308.16604 , primaryClass =

Pith/arXiv arXiv 2023

[3] [3]

Nature , keywords =

A census of baryons in the Universe from localized fast radio bursts. Nature , keywords =. doi:10.1038/s41586-020-2300-2 , archivePrefix =. 2005.13161 , primaryClass =

Pith/arXiv arXiv 2005

[4] [4]

PRL , keywords =

Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter. PRL , keywords =. doi:10.1103/PhysRevLett.117.091301 , archivePrefix =. 1605.00008 , primaryClass =

Pith/arXiv arXiv

[5] [5]

PRD , keywords =

Constraining primordial black holes using fast radio burst gravitational-lens interferometry with CHIME/FRB. PRD , keywords =. doi:10.1103/PhysRevD.106.043017 , archivePrefix =. 2204.06001 , primaryClass =

Pith/arXiv arXiv

[6] [6]

, keywords =

The Fast Radio Burst-emitting Magnetar SGR 1935+2154-Proper Motion and Variability from Long-term Hubble Space Telescope Monitoring. , keywords =. doi:10.3847/1538-4357/ac432f , archivePrefix =. 2112.07023 , primaryClass =

Pith/arXiv arXiv 1935

[7] [7]

, keywords =

A living theory catalogue for fast radio bursts. , keywords =. doi:10.1016/j.physrep.2019.06.003 , archivePrefix =. 1810.05836 , primaryClass =

Pith/arXiv arXiv 2019

[8] [8]

, keywords =

The First CHIME/FRB Fast Radio Burst Catalog. , keywords =. doi:10.3847/1538-4365/ac33ab , archivePrefix =. 2106.04352 , primaryClass =

Pith/arXiv arXiv

[9] [9]

, keywords =

A fast radio burst associated with a Galactic magnetar. , keywords =. doi:10.1038/s41586-020-2872-x , archivePrefix =. 2005.10828 , primaryClass =

Pith/arXiv arXiv 2005

[10] [10]

, keywords =

A bright millisecond-duration radio burst from a Galactic magnetar. , keywords =. doi:10.1038/s41586-020-2863-y , archivePrefix =. 2005.10324 , primaryClass =

Pith/arXiv arXiv 2005

[11] [11]

, keywords =

First Constraints on Compact Dark Matter from Fast Radio Burst Microstructure. , keywords =. doi:10.3847/1538-4357/aba7bb , archivePrefix =. 2002.12533 , primaryClass =

Pith/arXiv arXiv 2002

Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Core claim

Load-bearing premise

What would settle it