REVIEW 3 major objections 2 minor 2 cited by
Hubble constant constraint using 117 FRBs with a more accurate probability density function for ${\rm DM}_{\rm diff}$
T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash
Pith's one-line read A commonly used approximation for the scatter in FRB dispersion measures fails at low redshift; this paper derives the exact scatter and finds H0 ≈ 66.9 km/s/Mpc from 117 localized FRBs.
desk verdict Potentially important correction to a standard FRB likelihood approximation, but the abstract alone does not support the load-bearing claim and the referee should demand validation of p_diff and a head-to-head comparison. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The key object is $p_{\rm diff}$, the probability density function of ${\rm DM}_{\rm diff}$—the dispersion measure contributed by diffuse electrons in the intergalactic medium. The paper treats $\sigma_{\rm diff}$, the 'effective standard deviation' of this distribution, not as a free parameter to be guessed by a scaling law but as a computable quantity derived from $p_{\rm diff}$ itself. The corrected $\sigma_{\rm diff}$ is then inserted into a rewritten Gaussian-like likelihood for the DM–redshift relation; this avoids the low-redshift bias introduced by the $F/\sqrt{z}$ shortcut.
What would settle it
Measure the dispersion-measure scatter of a sample of low-redshift (e.g. $z \lesssim 0.1$) FRBs with precise host redshifts. If the observed scatter of ${\rm DM}_{\rm diff}$ tracks $F/\sqrt{z}$ more closely than the paper's distribution-derived $\sigma_{\rm diff}$, the correction is not the true standard deviation and the claimed bias is absent.
Extended reading notes
Core claim
The paper's central claim is that the parameter $\sigma_{\rm diff}$ appearing in the probability density function $p_{\rm diff}$ for the diffuse electron contribution to FRB dispersion measure has been mis-estimated by the widespread approximation $\sigma_{\rm diff} \simeq F/\sqrt{z}$. The paper shows this shortcut is valid only under contrived assumptions and deviates most from the true standard deviation at low redshift. It therefore derives $\sigma_{\rm diff}$ from the variance of $p_{\rm diff}$ and writes a more accurate likelihood for the FRB DM–redshift relation. Using 117 localized FRBs, the updated likelihood, combined with CMB data and taking $f_{\rm diff}=0.84$, yields $H_0 \Omega_
Load-bearing premise
The argument stands on whether the chosen $p_{\rm diff}$ really describes the scatter of diffuse-electron dispersion along FRB sightlines; if that distribution is wrong, the corrected $\sigma_{\rm diff}$ is still biased, and the cleaned separation of ${\rm DM}_{\rm diff}$ from host-galaxy and Milky Way foregrounds must also hold for all 117 FRBs.
Editorial extensions
If this is right
- FRB cosmological constraints that used $\sigma_{\rm diff}\sim F/\sqrt{z}$ are systematically biased, with the largest error at low redshift.
- Future FRB likelihood analyses should derive $\sigma_{\rm diff}$ from the assumed $p_{\rm diff}$ rather than a scaling shortcut.
- With 117 localized FRBs, the corrected method yields $H_0=66.889^{+6.754}_{-5.459}$ km s$^{-1}$ Mpc$^{-1}$ (for $f_{\rm diff}=0.84$ when combined with CMB), consistent with Planck-era values.
- The fully analytical correction remains valid and improves in precision as more localized FRBs are added.
Reading between the lines
- If $p_{\rm diff}$ itself is calibrated to simulations that mis-model the clumpy baryon distribution, the corrected $\sigma_{\rm diff}$ inherits that systematics; the paper abstracts away this dependency.
- A natural test is to split the 117 FRBs by redshift: the corrected likelihood should mainly change low-redshift constraints relative to the shortcut, so comparing high- and low-z subsamples would expose residual bias.
- The same corrected $\sigma_{\rm diff}$ can be applied to joint analyses with other cosmic probes (e.g., gravitational-wave standard sirens or supernovae) where FRBs enter as an independent baryon tracer.
- As the localized FRB sample grows past several hundred, the low-redshift deviation of the shortcut becomes statistically significant, so this correction will matter even more.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper analyzes 117 localized fast radio bursts (FRBs) and argues that the commonly used approximation sigma_diff ~ F/sqrt(z) for the diffuse electron dispersion measure is inaccurate, especially at low redshift. It proposes instead to compute sigma_diff directly from a more accurate probability density function p_diff for DM_diff and rewrites the likelihood accordingly. Combining the resulting FRB likelihood with CMB data and fixing f_diff = 0.84, it reports H0 Omega_b f_diff = 2.813_{-0.258}^{+0.250} km/s/Mpc and H0 = 66.889_{-5.459}^{+6.754} km/s/Mpc. The abstract claims a fully analytical correction that yields better constraints, but no derivation, validation, or comparison against the previous approximation is shown in the abstract.
Significance. If the proposed correction is valid, it would be a useful methodological improvement for FRB cosmology: published FRB constraints that rely on sigma_diff ~ F/sqrt(z) could be biased, and the corrected treatment would matter as the localized-FRB sample grows. The reported H0 is consistent with Planck, suggesting that the correction could reduce tension claims based on FRB samples. However, the paper's significance cannot be assessed from the abstract alone: the central improvement is a claim about the correct scatter model for DM_diff, and that claim requires validation against simulations or empirical residuals. The paper has not yet demonstrated that its corrected sigma_diff is more faithful to the true sightline variance than the approximation it criticizes.
major comments (3)
- [Abstract — definition and origin of p_diff] The load-bearing assumption is that p_diff is the correct distribution of the diffuse electron DM. The abstract states that sigma_diff is derived from p_diff, but it does not state where p_diff comes from, how it is calibrated, or how its redshift dependence and scatter model were chosen. If p_diff is wrong, the derived 'true' sigma_diff is still biased, and the reported H0 shift is unsupported. The paper must specify p_diff explicitly, justify it with simulations or independent data, and test whether the resulting sigma_diff matches the scatter in the 117-FRB residuals.
- [Abstract — H0 result and foreground/host subtraction] The reported H0 = 66.889_{-5.459}^{+6.754} km/s/Mpc depends on separating DM_diff from Milky Way and host-galaxy contributions in all 117 FRBs. The abstract does not describe this separation, nor does it discuss correlated errors or selection effects. Low-redshift FRBs, where the claimed deviation is largest, are exactly where host-galaxy and local-environment contributions can dominate; without a demonstrated clean separation, the low-z signal could be an artifact. The paper should present the sample selection, the foreground model, and a systematics budget.
- [Abstract — comparison and validation of the claimed improvement] The abstract claims 'better constraints' and says the old approximation 'only works under contrived assumptions,' but it gives no quantitative comparison. The paper should show, on the same 117 FRBs, the difference between the old likelihood and the new one, including the resulting H0 shift and uncertainty change. It should also include mock or simulation-based tests demonstrating that the new sigma_diff recovers the true scatter and that the uncertainty estimates are calibrated. Without such evidence, the 'fully analytical correction' is an analytic reparametrization of an assumed distribution rather than a validated improvement.
minor comments (2)
- [Abstract — wording] The phrase 'once thoughts as effective standard deviation' is unclear and appears to contain a typo; it should be reworded to 'previously treated as an effective standard deviation'.
- [General — accessibility of derivation] The abstract promises a derivation but gives no equation numbers or outline. If the full paper contains the derivation, the abstract should at least reference the relevant section so that readers can verify the claimed analytical correction.
Circularity Check
No significant circularity: the correction is analytical from an assumed p_diff, not fitted from the same data.
full rationale
The derivation chain is: (1) assume a form for p_diff, the probability density of the diffuse electron DM; (2) compute the standard deviation sigma_diff from that assumed p_diff analytically; (3) use this sigma_diff in the FRB likelihood to constrain H0 Omega_b f_diff; (4) optionally combine with CMB and fix f_diff = 0.84 to report H0. None of these steps reduces to its own input by construction. The reported constraint is not a renamed fit of p_diff to the same 117 FRBs; rather, p_diff is an independent modeling input. If p_diff is unvalidated or wrong, the derived sigma_diff and downstream H0 constraint could be biased, but that is an empirical/modeling concern, not a circularity in the logical chain. There is no evidence in the abstract of a fitted parameter being presented as a prediction, no self-citation used as load-bearing external support, and no uniqueness theorem imported from the authors' prior work. The abstract's phrase 'fully analytical correction' further supports that the correction is derived from p_diff rather than tuned to reproduce the target result. Therefore the paper does not exhibit circularity on the available evidence.
Assumptions & free parameters
free parameters (2)
- f_diff =
0.84 (adopted)
- F (coefficient of the critiqued approximation σ_diff ~ F/√z)
assumptions (4)
- domain assumption The assumed functional form of p_diff (probability density of the diffuse-electron DM term) is a correct description of the true DM_diff distribution along FRB sightlines, including its redshift evolution and scatter.
- domain assumption FRB dispersion measures cleanly decompose into diffuse IGM (DM_diff), host-galaxy, and foreground components, and the non-diffuse terms are modeled or subtracted without significant bias.
- domain assumption The sample of 117 localized FRBs is representative for cosmology; selection does not correlate with DM or redshift in a way that biases the likelihood.
- standard math Standard probability identities are valid for computing the standard deviation σ_diff from the density p_diff.
Cite this review
Pith. "Pith review of Hubble constant constraint using 117 FRBs with a more accurate probability density function for ${\rm DM}_{\rm diff}$." pith.science (2026). https://pith.science/paper/7PZCIKTM
@misc{pith2026250805161,
author = {Pith},
title = {Pith review of: Hubble constant constraint using 117 FRBs with a more accurate probability density function for $\rm DM_\rm diff$},
year = {2026},
howpublished = {\url{https://pith.science/paper/7PZCIKTM}},
note = {Machine review of arXiv:2508.05161}
}
abstract
Fast radio bursts (FRBs) are among the most mysterious astronomical transients. Due to their short durations and cosmological distances, their dispersion measure (DM) - redshift ($z$) relation is useful for constraining cosmological parameters and detecting the baryons in the Universe. The increasing number of localized FRBs in recent years has provided more precise constraints on these parameters. However, the larger dataset reveals limitations in the widely used probability density function ($p_{\rm diff}$) for ${\rm DM}_{\rm diff}$, which refers to the diffuse electron term of FRB DM. In this project, we collect 117 of the latest, localized FRBs, discuss the effect of a more accurate $\sigma_{\rm diff}$, which is a parameter in $p_{\rm diff}$ and once thoughts as ``effective standard deviation'', and more clearly rewrite their likelihood to better constrain the parameters above. We find that the widely used approximation $\sigma_{\rm diff} \sim F/\sqrt{z}$ only works under contrived assumptions and shows the greatest deviation from the true standard deviation in low redshift. In general, one should use an accurate method to derive this parameter from $p_{\rm diff}$. Our method yields better constraints on $H_0\Omega_b f_{\rm diff} = 2.813_{-0.258}^{+0.250}\;{\rm km/s/Mpc}$ or $H_0 = 66.889_{-5.459}^{+6.754} \;{\rm km/s/Mpc}$ when combining the FRB data with CMB measurements and taking $f_{\rm diff} = 0.84$. This fully analytical correction helps us better constrain cosmological parameters with the increasing number of localized FRBs available today.
Forward citations
Cited by 2 Pith papers
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Hierarchical Bayesian analysis of CHIME/FRB finds the FRB volumetric rate peaks with the cosmic star-formation history at mean delays of 0.1–0.3 Gyr, consistent with zero delay and ruling out multi-Gyr merger-like delays.
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Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO
LOFAR2.0, FAST Core Array and BINGO can constrain the PBH dark matter fraction f_PBH below 0.16-0.39 for masses above 10^{-2} to 10 solar masses via FRB lensing statistics.
Reviewed August 5, 2026 · model on record in the stance chip above.
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