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 →
T0 review · deepseek-v4-flash
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 →
Understanding constraints on primordial mass black holes made of dark matter using fast radio bursts
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
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.
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
- 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.
Referee Report
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
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
free parameters (5)
- κ (modified gravity parameter) =
0, 10⁻³⁰, 10⁻²⁵, 10⁻²⁰ cm⁻² (plotted)
- DMHost (host galaxy dispersion) =
117 pc cm⁻³ (fixed mean)
- DMHalo (Galactic halo dispersion) =
≈ 50 pc cm⁻³
- Minimum time-delay cutoff Δt_min =
10⁻⁹ s
- Magnification cutoff μ_max =
1 < μ < S/N/3
axioms (5)
- ad hoc to paper The de Sitter–Schwarzschild metric Eq. (2.1) represents a generic scalar-tensor modified-gravity theory.
- domain assumption No FRB in the CHIME sample is confirmed to be lensed.
- domain assumption The Macquart mean relation (Eq. 2.4) gives DMIGM for each individual FRB.
- domain assumption Standard ΛCDM cosmology with the given H(z) is assumed when computing angular diameter distances and DMIGM.
- standard math Poisson statistics with zero observed lensed events correctly describe the lensing count.
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}
}
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
Reference graph
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discussion (0)
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