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Fast Radio Bursts as cosmological proxies: estimating the Hubble constant

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The dispersion measures of 97 localized fast radio bursts, after subtracting Milky Way and host-galaxy contributions, give a maximum-likelihood Hubble constant of 65.13 ± 2.52 km/s/Mpc, matching Planck and heading toward SH0ES-level…

desk verdict A useful catalog and a clear MLE exercise, but the paper's own mocks show the estimators are biased and the quoted errors are too small. read the letter →

arxiv 2502.08509 v1 pith:K3PM5QEF submitted 2025-02-12 astro-ph.CO astro-ph.HEgr-qc

Eduard Fernando Piratova-Moreno , Luz Ángela García , Carlos A. Benavides-Gallego , Carolina Cabrera This is my paper · ORCID
classification astro-ph.COastro-ph.HEgr-qc
keywords fastradioburstsdispersionmeasureHubbleconstanttensioncosmologicalprobesmaximumlikelihoodestimationmockcatalogsH(z)reconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the dispersion measures (DMs) of fast radio bursts can act as cosmological distance probes: the intergalactic-medium contribution to DM is proportional to $H_0$ times a redshift integral, so $H_0$ can be read off once the Milky Way and host-galaxy terms are subtracted. Using 97 localized FRBs, the maximum-likelihood estimate yields $H_0 = 65.13 \pm 2.52$ km/s/Mpc, a 3.9% measurement compatible with Planck 2018 and lower than the SH0ES value. Reconstructing $H(z)$ from assumed linear or power-law DM–redshift relations gives divergent values, 51.27 and 77.09 km/s/Mpc, exposing the method's current model dependence. Simulated catalogs of 500 FRBs push the MLE precision to 1.4%, the same order as SH0ES, which the paper takes as evidence that a fivefold increase in localized FRBs would make this an independent, competitively precise probe of the Hubble constant. The key caveat is that host-galaxy DM is assumed, not measured, for each burst.

What carries the argument

The central object is the observed dispersion-measure decomposition $\mathrm{DM}_{\rm obs} = \mathrm{DM}_{\rm IGM} + \mathrm{DM}_{\rm MW} + \mathrm{DM}_{\rm host}/(1+z)$, with the intergalactic term written as $\mathrm{DM}_{\rm IGM}(z) = \frac{3c\Omega_b H_0}{8\pi G m_p}\chi_e f_{\rm IGM}\int_0^z \frac{1+z'}{E(z')}\,dz'$. Because the prefactor in front of the integral is proportional to $H_0$, each burst's DM becomes a noisy measurement of $H_0$ once $\mathrm{DM}_{\rm MW}=100$ pc cm$^{-3}$ and $\mathrm{DM}_{\rm host}=100/(1+z)$ pc cm$^{-3}$ are subtracted. The paper also differentiates fitted linear and power-law $\mathrm{DM}_{\rm obs}(z)$ relations to build $H(z)$ and evaluate it at $z=0$, and it maximizes a Gaussian likelihood with $\sigma^2 = \sigma_{\rm MW}^2 + \sigma_{\rm host}^2 + \sigma_{\rm LSS}^2$ to extract the best $H_0$.

What would settle it

Rerun the maximum-likelihood analysis on the same 97 FRBs with the host-galaxy prior replaced by the log-normal distribution used in the mock catalog (geometric mean 40–80 pc cm$^{-3}$, scatter 0.4–1.0); if $H_0$ moves outside 65.13 ± 2.52 km/s/Mpc, the fixed host-DM assumption is falsified. Observationally, measuring host-galaxy DMs for a subset of localized FRBs via H$\alpha$ emission and comparing the mean with $100/(1+z)$ would settle the same question directly.

Watch

Extended reading notes

Core claim

The central claim is that the dispersion measure of a localized FRB, after subtracting the Milky Way's fixed 100 pc cm$^{-3}$ and a host-galaxy term of $100/(1+z)$ pc cm$^{-3}$ with $50/(1+z)$ scatter, leaves an intergalactic-medium component whose normalization is tied to $H_0$. Maximizing the Gaussian likelihood over 97 bursts gives $H_0 = 65.13 \pm 2.52$ km/s/Mpc, a 3.9% measurement consistent with Planck 2018 and well below the SH0ES value. Fitting a linear DM–$z$ relation and then evaluating $H(z)$ at $z=0$ gives $H_0 = 51.27^{+3.80}_{-3.31}$ km/s/Mpc, while a power-law fit gives $H_0 = 77.09^{+8.89}_{-7.64}$ km/s/Mpc, bracketing the Planck and SH0ES values and illustrating the systematic spread of the reconstruction approach. In 100 mock catalogs of 500 FRBs each, the MLE recovers $H_0 = 67.30 \pm 0.91$ km/s/Mpc (1.4% precision), matching the SH0ES precision, with the median ($66.10 \pm 1.89$) more robust than the arithmetic mean ($66.21 \pm 3.46$). The paper concludes that FRB DMs are a viable independent cosmological probe whose precision will improve steeply as the localized sample grows.

Load-bearing premise

The calculation assumes every FRB's host galaxy contributes a dispersion measure of $100/(1+z)$ pc cm$^{-3}$ with $50/(1+z)$ scatter and the Milky Way contributes 100 pc cm$^{-3}$, even though these are not measured for most bursts; if the true host-galaxy DM distribution differs, every derived $H_0$ shifts.

Editorial extensions

If this is right

  • A fivefold increase in localized FRBs would bring the maximum-likelihood precision to roughly 1.4%, comparable to the SH0ES measurement, giving an independent check on the Hubble tension.
  • The arithmetic mean of per-FRB $H_0$ values is the least reliable estimator (5.2% precision on mock data); the median and the maximum-likelihood estimator are preferred.
  • The current 97-burst sample may underestimate $H_0$: every method applied to mock catalogs returns a larger value than the same method applied to the observed catalog.
  • The linear and power-law DM–$z$ reconstructions give $H_0$ values on opposite sides of the Planck–SH0ES gap, so the functional form of the DM–$z$ relation must be pinned down before the method's accuracy can match its precision.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Since the mock catalogs use a log-normal host DM with geometric mean 40–80 pc cm$^{-3}$ while the real-data analysis assumes a fixed $100/(1+z)$ pc cm$^{-3}$, the quoted 1.4% mock precision likely omits a systematic that could shift the observed-data $H_0$; rerunning the MLE on the 97 bursts with the log-normal host prior would quantify this.
  • Independent host-galaxy DM measurements, for example from H$\alpha$ emission or resolved host imaging, could break the host-DM degeneracy and turn the FRB method into a genuinely assumption-light cosmological probe.
  • The paper's mock pipeline could be extended to joint fits with supernova and baryon acoustic oscillation data, where 500 FRBs would help constrain dark energy alongside $H_0$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper uses the dispersion measures (DMs) of 97 localized fast radio bursts (FRBs) to estimate the Hubble constant H0. It applies three estimators: an arithmetic mean of individual H0 values (H0 = 57.67 ± 11.99 km/s/Mpc), a maximum-likelihood estimate (H0 = 65.13 ± 2.52 km/s/Mpc), and a reconstruction of H(z) from fitted linear and power-law DM–z relations (H0 = 51.27 and 77.09 km/s/Mpc, respectively). The authors also generate 100 mock catalogs of 500 FRBs each and report Table 1: MLE 67.30 ± 0.91, arithmetic mean 66.21 ± 3.46, median 66.10 ± 1.89, linear H(z) 54.34 ± 1.57, and power-law H(z) 91.84 ± 1.82 km/s/Mpc. The abstract and conclusions emphasize that the mock MLE precision (1.4%) is comparable to SH0ES. The paper's central claim is that FRB DMs can provide a precision-competitive, independent constraint on H0.

Significance. If the analysis were sound, the paper would be a useful contribution: it assembles a current catalog of 97 localized FRBs, applies a standard likelihood machinery, and provides a concrete forecast that 500 localized FRBs could reach 1.4% statistical precision. The mock-testing framework is a genuine strength, as it exposes how each estimator behaves on controlled data. However, the paper's own mock results show that the estimators are biased at the claimed precision, and the host-galaxy DM treatment is internally inconsistent. The central numerical results therefore cannot be taken at face value; the significance of the paper depends on whether the systematics can be recalibrated.

major comments (4)
  1. [Section 4, Table 1] The mock validation does not support the claimed precision. With fiducial H0 = 70, the MLE returns 67.30 ± 0.91 km/s/Mpc, a 2.7 km/s/Mpc bias that is about 3σ of the quoted error, while the linear and power-law H(z) methods return 54.34 ± 1.57 and 91.84 ± 1.82 km/s/Mpc, missing the input by 16–22 km/s/Mpc. The 1.4% figure is thus the statistical scatter of the estimator, not its accuracy. The real-data result in Eq. (21) inherits the same unmodeled systematics. In particular, the real-data analysis assumes DMhost = 100/(1+z) pc cm^-3 (Eq. 4), whereas the mock input (Eq. 23) draws DMhost from a log-normal with mean 40–80 pc cm^-3, so the estimator's host-galaxy model is mismatched to the simulation. The pipeline must be recalibrated on mocks whose host-galaxy model matches the one applied to real data, and the quoted errors must include host-galaxy systematics.
  2. [Eqs. (16)–(17)] The derivative term 100/(1+z)^2 is inconsistent with the host-galaxy convention in Eqs. (3)–(4). In Eq. (13), the host term subtracted from DMobs is DMhost/(1+z); with Eq. (4), this is 100/(1+z)^2, whose derivative is 200/(1+z)^3. The denominator used in Eqs. (16)–(17) instead corresponds to a host contribution of 100/(1+z) in the observer frame, i.e., a redshift-independent rest-frame host DM of 100 pc cm^-3. Since the H0 values 51.27 and 77.09 are computed directly from this derivative, they must be re-derived under one consistent convention before they can be reported.
  3. [Section 3.3, Eq. (21)] The quoted H0 = 65.13 ± 2.52 km/s/Mpc is obtained from likelihood curvature at fixed DMhost, DMMW, and f_IGM assumptions. DMhost is not measured independently for most of the 97 bursts, so the scatter in Eq. (19) is a model assumption rather than a measured uncertainty. The analysis does not marginalize over DMhost, DMMW, or f_IGM, and the error bar therefore understates the total uncertainty. The compatibility with Planck is not a robust statement until a systematic-error budget is included.
  4. [Section 3.2, Eqs. (12)–(17)] The H(z) method fits DMobs(z) to the same 97 data points and then differentiates the fitted relation, so H0 at z=0 is a direct re-expression of the fitted slope and intercept. The quoted values 51.27 and 77.09 are not independent cosmological constraints but restatements of the assumed functional form; the large spread between them reflects the two arbitrary fitting functions rather than a measurement of H0. This should be stated explicitly, and the method should not be presented as a separate probe.
minor comments (5)
  1. [Data Availability] The Data Availability section reproduces MNRAS policy text but does not actually provide a data availability statement or a link to the catalog. The authors should supply the catalog as supplementary material or state a repository.
  2. [Table A1] The Reference column contains incomplete entries such as '2016' and '2020; 2023b', and several of these abbreviations cannot be unambiguously matched to the reference list. Please provide full citations or a dedicated reference key.
  3. [Conclusions] The Conclusions paragraph misstates Table 1: it reports 66.10 ± 3.46 km/s/Mpc for the median and 67.30 ± 1.89 km/s/Mpc for the MLE, whereas Table 1 gives 66.10 ± 1.89 and 67.30 ± 0.91 km/s/Mpc. The error bars in the conclusions should be corrected.
  4. [Eq. (8)] The factor 10^4 Ω_b h^2 appears without derivation; Eq. (7) uses Ω_b directly. Please clarify the notation and the relation between the two expressions.
  5. [General] There are several typographical issues, including 'FBRs' in Section 1 and the use of 'pccm−3' without spaces. Please standardize units and fix typos throughout.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity in the central H0 estimates; the paper's methods are ordinary parameter-inference procedures on the same catalog. Minor self-citations supply empirical DM-z model forms, but these are refit to the current 97-FRB sample and are not load-bearing circular inputs.

full rationale

The three estimators in this paper are standard inference procedures rather than circular reductions. The arithmetic mean (Eq. 9) inverts the physical DMIGM relation (Eq. 7) for each FRB and averages the results; the MLE (Eq. 18) maximizes a likelihood over H0 using the same physical model. In neither case is H0 defined through a quantity that was itself fitted to H0. The H(z) reconstruction (Eqs. 12, 16-17) fits empirical DM-z relations (Eqs. 14-15) to the 97 FRBs and then evaluates the derivative at z=0, so the quoted H0 values are deterministic functions of the fitted slope or normalization. This is algebraic propagation of a fitted relation through a formula, not the pattern in which a prediction is equivalent to the fitted input by construction: the DM-z fits do not take H0 as an input, and the mock-catalog exercise (fiducial H0=70) returns 54.34 and 91.84 km/s/Mpc from the two H(z) forms, showing that the derived H0 is not forced to reproduce an input value. The self-citations to Piratova-Moreno and Garcia (2024) introduce the linear and power-law DM-z model forms and select them based on earlier performance, but the parameters are refit here, and the linear form is also the external Macquart et al. relation. The mock catalogs are internal consistency checks; the reported biases (MLE 67.30 vs 70, linear 54.34, power-law 91.84) are accuracy or systematics concerns, not circularity. The internal inconsistency between the host-DM derivative term in Eqs. 16-17 and the host model in Eq. 4 is a mathematical error, not a circular reduction.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The H0 estimates rest on several fixed astrophysical inputs, most importantly the assumed host DM (100 pc cm^-3), Milky Way DM (100 pc cm^-3), IGM baryon fraction (0.84), and, for the H(z) method, the choice of linear versus power-law DM-z fitting functions. The mock tests show the fitting-function choice alone changes the recovered H0 by roughly 37 km/s/Mpc, so these inputs carry the central result.

free parameters (7)
  • DM_host = 100/(1+z) pc cm^-3 = 100/(1+z) pc cm^-3 (assumed)
    Equation (4) assumes every host contributes 100 pc cm^-3 divided by (1+z); no host galaxy data are used. Changing this value shifts all H0 estimates.
  • DM_MW = 100 pc cm^-3 = 100 pc cm^-3 (assumed)
    Section 2.1 picks 100 pc cm^-3 from a cited 50-100 range; affects derived excess DM and hence H0.
  • f_IGM = 0.84 = 0.84 (adopted)
    Baryon fraction in the intergalactic medium taken from Hagstotz et al. 2022; enters Eq. (7) linearly.
  • Linear DM-z fit parameters a, b = a = 959.32 +/- 73.12 pc cm^-3, b = 240.11 +/- 25.67 pc cm^-3
    Fitted to the 97 FRBs in Section 3.2; the derivative dDM_IGM/dz and hence H0 is determined by these fitted numbers.
  • Power-law DM-z fit parameters A, alpha = A = 297.25 +/- 17.90 pc cm^-3, alpha = 2.03 +/- 0.13
    Alternative fit to the same 97 FRBs; gives the different H0 = 77.09 in Eq. (17).
  • Mock redshift distribution parameter alpha=7 = 7 (adopted)
    Controls mock sample depth; affects the mock forecasts in Section 4 but not the observed-data estimates.
  • Uniform prior range for MLE H0 = [40, 100] km/s/Mpc
    Rectangular prior assumed in Section 3.3; since the likelihood is well-peaked inside this range, it has minor influence.
assumptions (5)
  • domain assumption Flat Lambda CDM with Planck 2020 cosmological parameters
    Standard cosmology assumed; the H0 estimate is not model-independent and uses Planck values for other parameters (Section 2.2 and throughout).
  • domain assumption DM_IGM is Gaussian distributed around the mean predicted by Eq. (7)
    Used in the likelihood and in mock generation (Section 2.2, Eq. 19 and Section 4).
  • domain assumption Host DM follows a log-normal distribution in mock catalogs
    Inconsistency between simulation and analysis assumptions affects mock bias (Eq. 23 vs Eq. 4).
  • ad hoc to paper The DM-z relation can be represented by a linear or power-law function and differentiated to recover H(z)
    The choice of functional form determines H0 at z=0; mock tests show these forms are biased, so this assumption is not supported (Section 3.2, Table 1).
  • domain assumption Redshift distribution f(z) ~ z^2 exp(-7z) in mock
    Adopted from Hagstotz et al. 2022; affects mock forecasts.

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Cite this review

Pith. "Pith review of Fast Radio Bursts as cosmological proxies: estimating the Hubble constant." pith.science (2026). https://pith.science/paper/K3PM5QEF

@misc{pith2026250208509,
  author       = {Pith},
  title        = {Pith review of: Fast Radio Bursts as cosmological proxies: estimating the Hubble constant},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3PM5QEF}},
  note         = {Machine review of arXiv:2502.08509}
}
abstract

One of the most challenging problems in cosmology is the Hubble tension, a discrepancy in the predicted expansion rate of the Universe. We leverage the sensitivity of the Dispersion Measure (DM) from Fast Radio Bursts (FRBs) with the Hubble factor to investigate the Hubble tension. We build a catalog of 98 localized FRBs and an independent mock catalog and employ 3 methods to calculate the best value of the $H_0$: i) the mean of $H_0$ values obtained through direct calculation, ii) the maximum likelihood estimate (MLE) and iii) the reconstruction of the cosmic expansion history $H(z)$ using two DM-$z$ relations. When the confirmed FRBs is employed, our predictions are compatible with reports from the Planck+2018, with $H_0=65.13\pm2.52\,\text{km/s/Mpc}$ and $57.67\pm11.99\,\text{km/s/Mpc}$ for MLE and the arithmetic mean, respectively. If we assume a linear and a power-law function for the DM-$z$ relation, our predictions for $H_0$ are $51.27^{+3.80}_{-3.31}\,\text{km/s/Mpc}$ and $77.09^{+8.89}_{-7.64}\,\text{km/s/Mpc}$, respectively. Using 100 mock catalogs of simulated FRBs, we obtain larger values for $H_0$ with all methods considered: $H_{0;\text{ Like}}=67.30\pm0.91\,\text{km/s/Mpc}$, $H_{0;\text{ Mean}}=66.21\pm3.46\,\text{km/s/Mpc}$, $H_{0;\text{ Median}}=66.10\pm1.89\,\text{km/s/Mpc}$, $H_{0;\text{Linear}}=54.34\pm1.57\,\text{km/s/Mpc}$ and $H_{0;\text{Power-law}}=91.84\pm1.82\,\text{km/s/Mpc}$ for the MLE, the arithmetic mean, and linear and power-law $\text{DM}-z$ relations, respectively. Our results for mock FRB catalogs increase the statistical precision, ranging from 1.4\% to 5.2\% for the MLE and arithmetic mean. Our result with the MLE applied to synthetic FRBs is at the same level of precision as reports from SH0ES. The increase in the number of confirmed FRBs will provide us, in combination with other observations, a robust prediction of the value of the Hubble constant.

Figures

Figures reproduced from arXiv: 2502.08509 by the authors.

Figure 1
Figure 1. The histogram represents the frequency distribution of 𝐻0 values derived from the data. Using the arithmetic mean, the value for the Hubble constant with 97 confirmed FRBs is 𝐻0 = 57.67 ± 11.99 km/s/Mpc. biguity in host galaxy localization, so we calculate with 97 FRBs. In the first method, the mean value obtained for 𝐻0 is based on the sensitivity of the IGM term to this parameter. The second method focuses on maxi… view at source ↗
Figure 2
Figure 2. The Gaussian distribution obtained from the direct calculation and its associated errors is compared with the values reported by the Planck Collaboration et al. (2020a) and Riess et al. (2022) measurements. The blue dotted lines are the errors estimated as one standard deviation. our predictions for 𝐻0 and its statistical precision will improve, and our forecast of this cosmological parameter will be more consistent… view at source ↗
Figure 4
Figure 4. Reconstruction of the dispersion measure and redshift for one realization out of the 100 mock datasets. Method 𝐻0 Statistical (km/s/Mpc) precision (%) Arithmetic mean 66.21 ± 3.46 5.2 Median 66.10 ± 1.89 2.9 MLE 67.30 ± 0.91 1.4 𝐻 (𝑧) Linear model 54.34 ± 1.57 2.9 Power-law model 91.84 ± 1.82 2.0 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constraining the Baryon Fraction in Extragalactic Diffuse Ionized Gas with 124 Localized Fast Radio Bursts

    astro-ph.CO 2025-06 conditional novelty 5.0 of 10

    Analyzing 92 localized FRBs with a Jacobian-corrected IGM dispersion PDF plus CMB, BAO, and supernova data gives f_IGM = 0.864 ± 0.041 (YMW16, ΛCDM); the abstract's '124 bursts, f_d > 90%' headline is not supported by...

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.