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Refined Constraints on the Hubble Constant from Localized FRBs with Assessment of Systematic Effects

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Ninety-five localized fast radio bursts pin the Hubble constant at 71.28 km/s/Mpc with 2.8 percent statistical uncertainty.

desk verdict A genuinely useful systematic sensitivity map for FRB-based H0, but the headline 2.8% measurement is statistical only and shifts by 2–4σ under the paper's own alternative model choices. read the letter →

arxiv 2507.18946 v1 pith:KAQ4RXMX submitted 2025-07-25 astro-ph.CO astro-ph.HE

Chenyuan Xu , Yi Feng , Jiaying Xu This is my paper · ORCID
classification astro-ph.COastro-ph.HE
keywords fastradioburstsHubbleconstanttensiondispersionmeasureMacquartrelationcosmologicalparametersbaryonicfeedbackGalactichalo
topics The Hubble Tension
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

Within the standard ΛCDM model, the paper seeks to establish that a carefully curated sample of 95 localized fast radio bursts, interpreted through the dispersion measure-redshift (Macquart) relation, gives $H_0 = 71.28^{+1.90}_{-2.08}$ km s$^{-1}$ Mpc$^{-1}$, a statistical uncertainty below 2.8 percent that the authors report as the smallest achieved so far with FRBs. The measurement matters because FRBs are an independent probe of cosmic expansion, and the value sits between the CMB estimate (67.66) and the local distance-ladder estimate (73.04) that define the Hubble tension. The paper's second, diagnostic aim is to explain why earlier FRB analyses disagreed: it traces the discrepancies to concrete modeling choices—the Milky Way electron density model, the Galactic halo contribution, the intergalactic baryon fraction, the amplitude of intergalactic density fluctuations, and the host-galaxy DM distribution—and quantifies how far each choice moves $H_0$.

What carries the argument

The central object is the Macquart relation, the statistical correlation between an FRB's observed dispersion measure and its redshift. After subtracting the Milky Way disk and halo contributions, the remaining extragalactic dispersion measure is the sum of a host-galaxy term, modeled as log-normal, and an intergalactic term whose mean scales roughly as $\Omega_b H_0 f_{\mathrm{IGM}} z$ at low redshift and whose scatter is $\sigma_{\mathrm{IGM}} = F z^{-0.5}$. The likelihood multiplies the skewed probability density for the intergalactic fluctuation by the log-normal probability density for the host-galaxy term, and MCMC sampling turns this product into a posterior for $H_0$ alone, with all other cosmological parameters fixed. This machinery converts a growing catalog of localized bursts into a single cosmological number, but it does so by depending on external inputs ($F$, $f_{\mathrm{IGM}}$, and the host DM parameters) that directly set the scale of the inferred $H_0$.

What would settle it

Measure the amplitude of intergalactic density fluctuations directly—for example, by comparing dispersion-measure scatter among many FRBs at the same redshift using an independent redshift indicator that does not assume $H_0$. If the true $F$ is near 0.32 rather than $10^{-0.75}$, the paper's Table 5 implies the central value would move from about 71 to about 81 km s$^{-1}$ Mpc$^{-1}$.

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Extended reading notes

Core claim

Within the standard ΛCDM framework, and using the Macquart dispersion measure-redshift relation, the paper reports $H_0 = 71.28^{+1.90}_{-2.08}$ km s$^{-1}$ Mpc$^{-1}$ from 95 of 117 localized FRBs. The retained sample excludes bursts with ambiguous host associations, bursts hosted by elliptical galaxies, and bursts at Galactic latitude $|b| \le 15^\circ$. The analysis fixes the background cosmology to Planck 2018 values, adopts the NE2001 Galactic electron density model, the direction-dependent YT2020 Galactic halo model, an intergalactic baryon fraction of 0.93, an IGM fluctuation amplitude $F = 10^{-0.75}$, and host-galaxy DM parameters fitted to simulations by burst type. The paper claims this is the lowest statistical uncertainty yet for an FRB-only measurement, about 2.8 percent, and demonstrates with controlled comparisons that the choice of $F$ and of the host DM distribution shifts $H_0$ by several $\sigma$, which it offers as the main explanation for the spread among earlier FRB studies.

Load-bearing premise

The quoted $H_0$ rests on the external inputs being right: the host-galaxy DM distribution and the IGM fluctuation amplitude $F = 10^{-0.75}$; the paper's own table shows that replacing either with plausible alternatives shifts $H_0$ by roughly 3 $\sigma$ or more.

Editorial extensions

If this is right

  • An FRB-only route to $H_0$ at roughly 2.8 percent statistical precision is now competitive with other single-probe estimates, so each new localized burst with a host redshift tightens the measurement rather than merely adding a data point.
  • The measured central value sits between the Planck and SH0ES values, with quoted errors reaching both regimes, so this data set does not break the Hubble tension; it adds an independent point that is compatible with either side at the quoted precision.
  • The analysis identifies the IGM fluctuation amplitude $F$, tied to baryonic feedback, and the host-galaxy DM distribution as the dominant systematic levers: reverting to $F = 0.32$ raises the inferred $H_0$ to about 80.7, while adopting a fixed log-normal host DM distribution with median 100 pc cm$^{-3}$ lowers it to about 61.2 on the one-off subset.
  • Adopting a Galactic latitude cut at $|b| > 15^\circ$ is recommended for FRB cosmology: it removes events with unphysical negative extragalactic dispersion measures and stabilizes the $H_0$ estimate against Galactic electron-density model errors.

Reading between the lines

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

  • If $F$ and the host DM distribution are as uncertain as the paper's own comparisons suggest, the true uncertainty on this $H_0$ is larger than the quoted statistical error; a joint analysis treating $F$, $f_{\mathrm{IGM}}$, and host parameters as free, with priors from independent probes, would likely return error bars closer to 8–10 km s$^{-1}$ Mpc$^{-1}$.
  • The strong coupling between $F$ and $H_0$ implies FRB-only Hubble constraints cannot be treated as feedback-free cosmological rulers; conversely, fixing $H_0$ externally could turn the same Macquart-relation likelihood into a competitive measurement of the baryon fluctuation amplitude and the diffuse baryon fraction.
  • A testable prediction of the YT2020 halo model is that future FRB sightlines toward the Galactic center should show systematically higher Milky Way halo dispersion measures; if pulsar-based halo measurements instead find no longitude dependence, the YT2020-based $H_0$ would need revision.
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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 constrains the Hubble constant from the dispersion measure-redshift relation of 95 localized fast radio bursts selected from an initial sample of 117 events. Using a fixed Planck18 background cosmology, NE2001 for the Galactic ISM, the YT2020 model for the Galactic halo, fIGM=0.93 from Connor et al. (2024), F=10^-0.75 from Baptista et al. (2024), and host-galaxy DM parameters from Zhang et al. (2020), the authors report H0 = 71.28^{+1.90}_{-2.08} km/s/Mpc and claim a statistical uncertainty below 2.8%, the lowest among relevant FRB studies. The paper then systematically examines the sensitivity of this result to outliers, Galactic electron density models, the Galactic halo contribution, fIGM, F, and the host-galaxy DM distribution, and shows that several alternative choices shift H0 by more than 2-3 sigma. The paper concludes that these systematic effects need careful treatment before FRBs can provide reliable cosmological constraints.

Significance. If the quoted measurement were robust, it would be a competitive FRB-only H0 determination at about 2.8% statistical precision, and the paper's systematic study is a genuine advance over previous work, which often adopts one set of nuisance parameters without testing alternatives. The explicit tabulation of how H0 shifts under different modeling choices in Tables 3-5, the use of a uniform latitude cut to remove unreliable low-latitude events, and the identification of the degeneracy between H0 and the IGM fluctuation amplitude F are useful contributions. However, the central claim as presented is conditional on point estimates of several external astrophysical parameters, and the paper does not fold the large shifts it documents into a final systematic error budget. This makes the current headline number a conditional estimate rather than a refined measurement with the stated uncertainty.

major comments (4)
  1. [Section 4.4, Table 5] The headline central value is conditional on point estimates for F and the host-galaxy DM distribution. The paper's own Table 5 shows that replacing F=10^-0.75 with F=0.32 shifts H0 from 70.89 to 80.68, a change of about 2.9 sigma, and that replacing the Zhang et al. (2020) host parameters with those of Fortunato et al. (2023) shifts H0 to 61.22, a change of more than 3 sigma. These shifts are larger than the quoted statistical uncertainty, so the 'statistical uncertainty below 2.8%' reported in the abstract is not the uncertainty of the measurement unless these nuisance parameters are marginalized over or an explicit systematic error is added to the final budget. The paper currently does neither.
  2. [Section 4.3, Table 4] The choice of the Galactic halo model also moves the result by more than the statistical error: fixing DMMW,halo=50 pc cm^-3 gives H0=63.75^{+1.83}_{-1.90}, a downward shift of more than 2.7 sigma relative to the fiducial YT2020-based value. Because the paper itself states that a constant halo model 'has not been conclusively ruled out,' the YT2020 choice cannot be treated as a known input. Some estimate of model uncertainty, such as a prior over halo models or a quoted systematic error, is needed before the central value can stand as a refined constraint.
  3. [Section 4.2, Table 3] The |b| cut is an analysis choice that affects the result: the NE2001-based H0 varies between 65.60^{+1.83}_{-1.80} and 71.28^{+1.90}_{-2.08} across the cuts tabulated, a spread of roughly 2.1 sigma, with the no-cut case giving 65.84^{+1.85}_{-1.70}. The paper states that results converge beyond |b|>15 degrees, but the table shows 69.87 at |b|>20 degrees and 69.95 at |b|>30 degrees, so the residual dependence on the cut should be quantified or included in the error budget rather than asserted to have converged.
  4. [Section 4.4, fIGM scaling] The claim that replacing fIGM=0.93 with fIGM=0.865 scales the result by a factor of 0.93/0.865 assumes a strict proportionality that holds only to first order in the likelihood. Since the paper elsewhere emphasizes that the IGM PDF is skewed and its mean and peak do not coincide, this scaling should be stated as an approximation and, ideally, checked by re-running the MCMC with the alternative fIGM value.
minor comments (5)
  1. [Equation (7)] Equation (5) defines a probability density for DMhost, but Equation (7) writes phost(DMhost,i | mu_host, sigma_host) without specifying that DMhost,i must be marginalized over the log-normal distribution in the convolution with pIGM. The notation should be defined explicitly to avoid ambiguity.
  2. [Appendix A, Table 6] Table 6 lists the full 117-FRB sample, but the final 95-FRB subset and the 85 one-off FRB subset used in Table 5 are not identified in the table. Please add a column or marker indicating which bursts enter each sample for reproducibility.
  3. [Section 3, Table 1] The MCMC settings are not reported: chain length, burn-in, number of walkers, and convergence checks are absent. Table 1 is labeled as a summary of settings, but it lists only astrophysical parameters and results, so the sampling details should be added for reproducibility.
  4. [Figure 1 caption] The caption states that DMMW,halo and DMhost are 'both assumed with 50 pc cm^-3', which is inconsistent with the fiducial analysis that adopts YT2020 and a log-normal host-galaxy distribution. The caption appears to describe only panel (a) with Macquart et al. (2020) settings, and this should be clarified.
  5. [Acknowledgments] The acknowledgments contain a duplicated word: 'supported by by the Leading Innovation and Entrepreneurship Team' should read 'supported by the Leading Innovation and Entrepreneurship Team'.

Circularity Check

2 steps flagged · score 4.0 of 10

H0 = 71.28 is partially inherited from FRB-calibrated nuisance parameters: fIGM and F are degenerate with H0 and were themselves estimated from FRB data, so the quoted 2.8% statistical error is conditional on those inputs.

  1. self definitional [Section 2 (fIGM bullet), Section 4.4, Eq. (3)]
    "On the observational side, Connor et al. (2024) analyzed FRB samples and obtained a value of fIGM = 0.93+0.04−0.05 ... Following the principle of relying on observational constraints whenever possible, we adopt the value fIGM ≃ 0.93 from Connor et al. (2024). ... if we adopt the value of fIGM = 0.865 reported by Zhang et al. (2025) instead of fIGM = 0.93 from Connor et al. (2024), our results would be scaled by a factor of (0.93/0.865)."

    In the Macquart relation (Eq. 3), DMIGM depends on H0 and fIGM in a degenerate combination, and the paper itself states that changing fIGM rescales the inferred H0 by the inverse ratio. The adopted fIGM was measured from FRB dispersion measures, i.e., from the same probe and the same relation that is now used to fit H0. Any such fIGM estimate is defined only relative to an assumed H0. Fixing an FRB-calibrated fIGM and fitting H0 to FRB data therefore amounts to recovering a rescaling of the H0 assumption built into the fIGM input (up to differences in sample and other fixed parameters). The headline value H0 = 71.28 is thus not a self-contained FRB measurement but a conditional estimate whose central value inherits an H0 choice from the fIGM calibration.

  2. other [Section 2 (σIGM bullet), Section 4.4, Table 5]
    "we follow the form σIGM = Fz −0.5 and adopt the observationally constrained value F = 10−0.75 from Baptista et al. (2024). ... We find that increasing F from 10−0.75 to 0.32 raises the inferred H0 by ∼ 2.9σ, while decreasing F from 10−0.75 to 0.09 lowers H0 by ∼ 3.9σ."

    Baptista et al. (2024) measured F jointly with H0 from FRB data; F is not an externally measured constant but a parameter from a previous FRB H0–F analysis. The paper fixes F to that best-fit point and then fits H0 as the only free parameter, while its own Table 5 shows that published alternative values of F shift H0 by 2.9–3.9σ. Because pIGM in Eq. (7) depends on both H0 (mean) and F (scatter), adopting a point estimate of F from a joint FRB H0 fit injects a correlated H0–F posterior into the new measurement. The quoted statistical error therefore omits the variance of this FRB-calibrated input, making the central claim a conditional estimate rather than a fully independent derivation.

full rationale

The H0 posterior is fit directly from the DM–z data with H0 as the only free parameter, so there is no construction-level equivalence between the fitted H0 and the raw data; the result is not, for example, a renamed fit of F or fIGM. However, the two most influential fixed inputs, fIGM and F, come from FRB-based analyses (Connor et al. 2024; Baptista et al. 2024) and are degenerate with H0 in the Macquart relation. The paper's own sensitivity tables (Tables 4–5) show that published alternative choices for F, host-DM, fIGM, and the Galactic halo shift H0 by 0.9–3.9σ, i.e., by more than the quoted statistical uncertainty. The paper is transparent about these systematics in Section 4.4, which is good practice, but it does not propagate any of these FRB-calibrated input uncertainties into the headline 2.8% error. The central claim is therefore partially circular: it is an H0 measurement conditional on nuisance parameters that were themselves estimated with FRBs under an assumed H0. The host-galaxy parameters from Zhang et al. (2020) are simulation-based rather than H0-derived, and the halo model YT2020 is X-ray-based, so the circularity is concentrated in fIGM and F. Overall score 4: substantial conditioning on same-probe inputs, but the 95-FRB data still carry independent information and the result is not forced to a single value by construction.

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

The central fit contains several hand-picked inputs with demonstrated strong effects on H0; no default model is derived from first principles in this paper. The absence of invented physical entities is notable, but the adopted nuisance parameters carry the model dependence.

free parameters (5)
  • H0 = 71.28 +1.90/-2.08 km/s/Mpc
    The target parameter, fit by MCMC with uniform prior U(50,90).
  • F (IGM fluctuation amplitude) = 10^-0.75
    Fixed to observational fit of Baptista et al. 2024; changing to 0.09 or 0.32 shifts H0 by 3.9 sigma and 2.9 sigma (Table 5).
  • fIGM (diffuse baryon fraction) = 0.93
    Fixed from Connor et al. 2024; paper notes switching to 0.865 would scale H0 by factor 0.93/0.865.
  • mu_host, sigma_host (host DM distribution) = redshift-dependent values from Zhang et al. 2020
    Fixed from IllustrisTNG fits; Fortunato et al. alternatives shift H0 by more than 3 sigma (Table 5).
  • Galactic latitude cut |b| = 15 degrees
    Chosen post hoc after inspecting negative DMEG events; H0 varies with cut in Table 3.
assumptions (5)
  • domain assumption Standard Lambda CDM with Planck18 fixed cosmology (Omega_m, Omega_Lambda, Omega_b)
    Used in Equation 3 and to convert DM to H0.
  • domain assumption Macquart relation Equation (3) for mean DMIGM with ionization fractions approximately 1 for z < 3
    Basis of the likelihood; taken from Deng and Zhang 2014 and Zhou et al. 2014.
  • domain assumption DMIGM scatter PDF Equation (4) with alpha = 3, beta = 3 and sigma_IGM = F z^-0.5
    Empirical model from McQuinn 2014 and Macquart et al. 2020; adopted rather than derived.
  • ad hoc to paper Log-normal DMhost distribution Equation (5) with parameters from IllustrisTNG
    Paper itself notes limited theoretical guarantees in Section 2, yet the central result depends on it.
  • domain assumption Galactic halo model YT2020 is accurate
    Direction-dependent halo contribution from X-ray data; constant halo alternatives shift H0 by 2.7 sigma (Table 4).

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Pith. "Pith review of Refined Constraints on the Hubble Constant from Localized FRBs with Assessment of Systematic Effects." pith.science (2026). https://pith.science/paper/KAQ4RXMX

@misc{pith2026250718946,
  author       = {Pith},
  title        = {Pith review of: Refined Constraints on the Hubble Constant from Localized FRBs with Assessment of Systematic Effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KAQ4RXMX}},
  note         = {Machine review of arXiv:2507.18946}
}
abstract

The dispersion measure-redshift relation of fast radio bursts (FRBs) provides a valuable cosmological probe for constraining the Hubble constant, offering an independent measurement that could help resolve the ongoing Hubble tension. In this paper, we begin with a sample of 117 localized FRBs and use 95 of them to constrain $H_0$ to $71.28^{+1.90}_{-2.08}$ km s$^{-1}$ Mpc$^{-1}$ within the standard Lambda Cold Dark Matter ($\Lambda$CDM) model. The resulting statistical uncertainty is below 2.8\%, improving previous FRB-based measurements and highlighting the promise of larger future samples. Beyond statistical improvements, we note that different parameter choices have been adopted in previous studies and some results show discrepancies in $H_0$. To address this issue, we perform a systematic assessment of modeling uncertainties that can affect the inferred value of $H_0$, including Galactic electron density models, the contribution of the Galactic halo, outliers such as FRB~20190520B located in extreme environments, and the other parameter selections. We also discuss possible approaches to mitigate these sources of uncertainty, emphasizing both the challenges and prospects of using FRBs as reliable cosmological tools.

Figures

Figures reproduced from arXiv: 2507.18946 by the authors.

Figure 1
Figure 1. (a) The Macquart relation of all FRBs used in this paper, DMMW,ISM is calculated with NE2001, DMMW,halo and DMhost are both assumed with 50 pc cm−3 , cosmology parameters are from Planck18 (Planck Collaboration et al. 2020) and F is set to 0.32 by following Macquart et al. (2020). (b) The H0 posteriori distribution obtained by 95 FRBs in this paper using NE2001, yielding H0 = 71.28+1.90 −2.08 km s−1 Mpc−1 . By compa… view at source ↗
Figure 2
Figure 2. (a) The DMEG of the 117 FRBs. The DMMW,halo is calculated with YT2020 model, and DMMW,ISM is from NE2001 and YMW16, the colorbar refers to Galactic latitudes. The cut of |b| > 15◦ can naturally remove the FRBs with negative DMEG, as well as those with large differences between NE2001 and YMW16. (b) The predicted DMs and real DMs of 189 pulsars with independently determined distances from ATNF v1.54. The colorbar ref… view at source ↗
Figure 3
Figure 3. (a) The H0 posteriori distribution of selecting FRBs by |b| > 20◦ , |b| > 15◦ , and no |b| cut. NE2001 is used as Galactic electron density model. (b) The H0 posteriori distribution of selecting FRBs by |b| > 20◦ , |b| > 15◦ , and no |b| cut. YMW16 is used as Galactic electron density model [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: (a) The H0 posteriori distribution by using different values for DMMW,halo. (b) The DMMW,halo posteriori distribution by using U(10, 120) as prior, and the histogram of predicted DMMW,halo by YT2020. (c) The direction-dependence of predicted DMMW,halo by YT2020 [PITH_…
Figure 5
Figure 5. Figure 5: (a) The H0 posteriori distribution when using different µhost and σhost on 85 one-off FRBs. The blue line use the µhost and σhost provided by Zhang et al. (2020), which are sightly dependent on redshift; the red line use µhost = ln(100) and σhost = 0.434, which are ass…
Figure 6
Figure 6. Figure 6: (a) Posteriori of H0 posteriori for three different values of F on 85 one-off FRBs, showing that larger F shifts H0 higher. (b) Probability density functions of DMIGM at z = 0.2, illustrating the degeneracy between H0 and F: H0 shifts the distribution horizontally, whi…

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