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REVIEW 5 major objections 7 minor 88 references

Estimating the baryon fraction in the IGM from well-localized FRBs and DESI data

T0 review · 5 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Using 107 well-localized fast radio bursts and model-independent distances from DESI BAO and two supernova catalogs, this paper estimates the intergalactic-medium baryon fraction at fIGM,0 ≈ 0.99 and finds only weak evidence that it…

desk verdict A transparent, incremental extension of the author's earlier FRB method to 107 events; the no-evolution conclusion is solid, but the headline fIGM ~ 0.99 sits at the physical boundary and depends on a single-parameter host-DM model that needs a robustness test. read the letter →

arxiv 2507.17693 v1 pith:GSLA6XFO submitted 2025-07-23 astro-ph.CO

Thais Lemos This is my paper · ORCID
classification astro-ph.CO PACS 98.80.-k
keywords fastradioburstsbaryonfractionintergalacticmediumdispersionmeasureDESIacousticoscillationstypeIasupernovaecosmologicalmodelindependencemissingbaryons
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 tries to pin down the fraction of cosmic baryons that live in the intergalactic medium, $f_{\mathrm{IGM}}$, by combining the dispersion measures of 107 well-localized fast radio bursts with distance measurements from DESI BAO and two Type Ia supernova catalogs. Its central move is a relation that rewrites the IGM dispersion measure in terms of luminosity distance, so distances are taken from the data rather than from a chosen cosmological model. For a constant baryon fraction the authors find $f_{\mathrm{IGM},0} \sim 0.99^{+0.01}_{-0.07}$ at $1\sigma$, with a mean host-galaxy dispersion contribution near $113$ pc/cm$^3$. A Bayesian model comparison between the constant case and an evolving parameterization yields only weak evidence, so the current FRB sample cannot decisively say whether $f_{\mathrm{IGM}}$ changes with redshift. The result matters because it bears on the long-standing 'missing baryons' problem and shows that FRB dispersion measures can act as an independent, model-light census of cosmic baryons.

What carries the argument

The load-bearing object is the dispersion-measure relation obtained by integrating Eq. (2.3) by parts and writing the Hubble parameter in terms of luminosity distance $D_L$, so that $\mathrm{DM}_{\mathrm{IGM}}$ depends on $D_L(z)$ and an integral of $D_L(z')/(1+z')$ rather than on an assumed cosmology. Distance–redshift curves are reconstructed non-parametrically from the BAO and supernova catalogs with Gaussian processes, and the free parameters — $f_{\mathrm{IGM},0}$ and $\mathrm{DM}_{\mathrm{host},0}$, plus $\alpha$ in the evolving case — are fit by MCMC. The host-galaxy dispersion enters through a single global parameter $\mathrm{DM}_{\mathrm{host},0}$ scaled by $(1+z)$, and the cosmic-web scatter in electron density is folded in as $\delta = 230\sqrt{z}$ pc/cm$^3$.

What would settle it

Measure host-galaxy dispersion independently for a subset of the 107 FRBs, for instance from host-galaxy emission measures or from scattering screens in repeating bursts, and compare the resulting distribution to the single fitted value near 113 pc/cm$^3$; if the measured mean or median differs by more than the quoted 12 pc/cm$^3$ uncertainty, or if the host-DM distribution is strongly asymmetric, the constant-case $f_{\mathrm{IGM},0} \approx 0.99$ is not robust and the single-parameter host model must be replaced.

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Extended reading notes

Core claim

The paper's claim is that the observed extragalactic dispersion measures of 107 well-localized FRBs, combined with luminosity distances reconstructed from DESI DR2, DES Y5, and Pantheon+, give $f_{\mathrm{IGM},0} \sim 0.99$ at $1\sigma$ for the constant parameterization, with the host-galaxy contribution $\mathrm{DM}_{\mathrm{host},0}$ around $112{-}116$ pc/cm$^3$, and that these values are mutually consistent across the three independent distance datasets. For the time-dependent parameterization $f_{\mathrm{IGM}}(z) = f_{\mathrm{IGM},0} + \alpha z/(1+z)$, the recovered $f_{\mathrm{IGM},0}$ values are lower but statistically compatible at $2\sigma$, and $\alpha$ is consistent with zero within the quoted errors. The Bayesian evidence comparison gives log-Bayes factors of $-0.53$, $-0.71$, and $+0.34$ for the three datasets, all in the inconclusive-to-weak range, which the authors read as meaning that a conclusive answer about the time evolution of $f_{\mathrm{IGM}}$ cannot be achieved from the current FRB data, with weak evidence favoring the constant case in two of the three combinations.

Load-bearing premise

The estimate rests on treating host-galaxy dispersion as a single global parameter, $\mathrm{DM}_{\mathrm{host},0}$ times $(1+z)$; in reality host galaxies vary widely in gas content, orientation, and local plasma, and if that spread is broad or skewed the inferred IGM baryon fraction could shift.

Editorial extensions

If this is right

  • If $f_{\mathrm{IGM},0} \approx 0.99$ is correct, the intergalactic medium at low redshift holds essentially all baryons predicted by big-bang nucleosynthesis, effectively closing the low-redshift 'missing baryons' budget.
  • The estimated host-galaxy dispersion, $\mathrm{DM}_{\mathrm{host},0} \sim 112{-}116$ pc/cm$^3$, gives a quantitative prior for modeling FRB host environments and for separating host and IGM contributions in future samples.
  • Distinguishing a constant from an evolving $f_{\mathrm{IGM}}$ will require many more localized FRBs rather than more precise distance catalogs, because the current Bayes factors are all in the weak-evidence regime.
  • Since DESI, DES Y5, and Pantheon+ yield consistent $f_{\mathrm{IGM}}$ values despite disagreeing on dark-energy parameters, the probe is insensitive to the very cosmological tensions motivating it.

Reading between the lines

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

  • A natural extension is to replace the single host-DM parameter with a population distribution — e.g., a log-normal with scatter estimated from the observed spread in host-galaxy dispersion — to test whether $f_{\mathrm{IGM},0} \approx 0.99$ survives when host variation is modeled rather than averaged away.
  • The sign flip of the Bayes factor between Pantheon+ and the other two datasets suggests that the distance reconstruction, such as which supernova sample or Gaussian-process kernel is used, may be influencing model preference; checking this would clarify whether evolution claims are data-driven or method-driven.
  • If a thousand-scale localized FRB sample pushed $f_{\mathrm{IGM}}$ toward unity at all redshifts, the baryon census problem would shift from 'missing baryons in the IGM' to locating the remaining baryons in galaxies, halos, and the warm-hot phase, a map FRB statistics could provide directly.
  • The same $D_L$-based rewriting could be applied to the transverse comoving distance from future BAO or gravitational-wave standard siren measurements, making the probe applicable to datasets where supernova distances are not available.
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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

5 major / 7 minor

Summary. This paper constrains the baryon fraction in the IGM, fIGM, by combining 107 well-localized fast radio bursts with distance information from DESI DR2 BAO transverse-mode measurements and from the Pantheon+ and DES Y5 supernova samples. Using the integration-by-parts method of the author's previous work, the dispersion measure of the IGM is re-expressed in terms of luminosity distance, and two models are fitted: a constant fIGM,0 and a time-dependent fIGM(z)=fIGM,0+alpha z/(1+z), with a shared host-galaxy DM parameter. For the constant case the paper reports fIGM,0 about 0.99 with host DM around 113 pc/cm3; for the time-dependent case it reports fIGM,0 around 0.94-0.97 and alpha around 0.6-0.7. A Bayesian model selection analysis gives |ln B| between 0.34 and 0.71, from which the paper concludes that a conclusive answer about fIGM evolution cannot be obtained from current FRB data. The central derivation in Section 3.2 appears correct, but several statistical modeling choices affect the quantitative headline values.

Significance. If the quantitative estimates survive robustness checks, the method provides a useful cosmology-independent cross-check of the baryon inventory and of IGM ionization at z<1, and the use of three independent distance datasets is a genuine strength. The paper is appropriately cautious in its main model-selection conclusion: the small Bayes factors do support the statement that current data are inconclusive about fIGM evolution. However, the headline constant-case value fIGM,0=0.999 sits at the physical boundary fIGM<=1 and rests on a single-parameter host-DM model, and the analysis also contains several reproducibility and error-propagation gaps. The qualitative conclusions are defensible, but the quantitative headline is not yet secure.

major comments (5)
  1. [Section 2, Eq. (2.2); Section 3.1.1, Eq. (3.1)] The host-galaxy contribution is modeled by a single global parameter DMhost,0 with a fixed 30 pc/cm3 Gaussian scatter. Host DM is known to vary with galaxy type, inclination, star formation, and local plasma; excluding FRB 20190520B removes one extreme object but does not model the remaining scatter. Since the constant-case posterior peaks at fIGM,0=0.999 (Table 1), the inferred fIGM,0 is sensitive to this host-DM model. Please add a robustness test that marginalizes over a free sigma_host,0 or uses measured host-DM estimates where available, and show how fIGM,0 and its uncertainty change.
  2. [Section 3.2; Table 1] The prior ranges for fIGM,0, alpha, and DMhost,0 are not stated. The constant-case estimate fIGM,0=0.999 with upper error 0.007-0.010 sits at the edge of the physically allowed region fIGM<=1, so the quoted upper error and the agreement with fIGM=1 are sensitive to prior truncation. Please report the exact priors and quantify the boundary effect, for example by testing a prior extending above unity or by reporting the posterior mass within a small interval of fIGM,0=1.
  3. [Section 3.1.1; Table 3] For 41 FRBs, sigma_obs is randomly drawn from a Gaussian whose mean and standard deviation are computed from the other events, but no random seed or draw is documented. Because sigma_obs enters the likelihood through sigma_tot in Eq. (3.1), the quoted parameter intervals and Bayes factors are not reproducible and may depend on the particular realization. Please publish the seed and draws, or marginalize over the missing sigma_obs with a stated prior, and confirm that the central estimates are stable.
  4. [Section 3.2, Eq. (3.2)] Equation (3.2) gives sigma_IGM = A fIGM,0 sqrt(sigma_DL^2/c^2 + sigma_I^2/c^2), which is the error propagation for the constant case. For the time-dependent model in Eq. (3.7), the coefficient of sigma_DL is A[fIGM,0 + alpha z/(1+z)] and the coefficient of sigma_I is A(fIGM,0 + alpha). Using A fIGM,0 for both terms underestimates the IGM variance in the time-dependent case and can bias alpha and the associated evidence. Please propagate the uncertainties directly from Eq. (3.7).
  5. [Section 3.1.1; Section 4] The value delta = 230 sqrt(z) pc/cm3 is fixed, and Section 4 attributes the difference from the previous [18] results to exactly this choice. Since delta enters every sigma_tot in Eq. (3.1), the error bars and Bayes factors in Tables 1 and 2 are conditional on this single ad hoc noise model. The previous paper varied delta; the present analysis should either provide a sensitivity scan over delta or justify the fixed value, otherwise the reported uncertainties are not robust to a key modeling assumption.
minor comments (7)
  1. [Section 4; Table 2; Conclusions] The model-selection language is not consistent with the Jeffreys' scale stated in Section 4: the reported values |ln B| = 0.34, 0.53, and 0.71 fall in the 'inconclusive' range (0-1), not 'weak evidence' as stated in the abstract and conclusions. Please revise the wording to say the evidence is inconclusive.
  2. [Section 3.1.1] In the list of excluded FRBs, the third low-redshift event is printed as 'FRB [35]' with no event name; please insert the correct identifier.
  3. [Section 3.1.1] Equation (3.2) refers to 'Eq. 3.9' for sigma_I, but no Eq. (3.9) appears in the manuscript; either number the integral after Eq. (3.8) or refer to it directly.
  4. [Table 3] The text says that 41 FRBs are marked with the symbol dagger in the sigma_obs column, but the table as presented does not show these markers; please ensure they are visible in the published table.
  5. [Section 5] The conclusions refer to 'FRB + DES' instead of 'FRB + DES Y5'; please use consistent dataset labels throughout.
  6. [Footnote 6] Footnote 6 contains 'MBMB' instead of 'MB'; please fix the typo.
  7. [Section 3.2] The Gaussian Process reconstruction produces a joint predictive distribution for DL at the FRB redshifts, but the paper does not state whether correlations between reconstructed DL values, or between DL and the integral in Eqs. (3.7)-(3.8), are propagated into sigma_IGM. Please clarify this point or justify the diagonal approximation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DM_IGM expressions are re-derived from the standard dispersion-measure formula and the fitted f_IGM is estimated from external FRB, SNe and BAO data.

full rationale

The paper's central derivation is self-contained. Equation (2.3) is the standard DM_IGM integral, and Eqs. (3.7) and (3.8) are obtained from it by integration by parts after rewriting H(z) in terms of the luminosity distance, with the algebra displayed in the text. The target quantity f_IGM is not an input to these equations. The luminosity distances are external: they come from SNe catalogs (Pantheon+, DES Y5) and DESI DR2 BAO data via Gaussian-process reconstruction, and fixed calibrations (H0 from SH0ES, MB matching that H0, Ωbh^2 from BBN, rd from Verde et al.) do not depend on f_IGM. The host-galaxy contribution is a free parameter, DMhost,0, so the host model is not a fitted input renamed as a prediction. The authors cite their previous paper [18] for the method, but Section 3.2 fully reproduces the derivation, and the adopted fluctuation δ=230√z pc/cm3 is an input traced to [18,20], not the target result. The Bayesian model comparison is computed from the fitted likelihood using MultiNest and does not presuppose the posterior preference. Remaining concerns—single-parameter host-DM modeling, random draws for 41 missing σobs values, and the fIGM≤1 prior boundary—are robustness and correctness issues, not circularity. I therefore find no step in which a claimed prediction reduces by construction to its inputs or to a load-bearing self-citation.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The result is not a first-principles prediction; it is a fit with three model parameters (fIGM,0, alpha, DMhost,0) plus several fixed astrophysical inputs. The fixed fluctuation amplitude delta=230 sqrt(z) and the global host parameter are the largest modeling choices. The model comparison also depends on prior bounds alpha >= 0 and fIGM <= 1, which are not fully specified or tested.

free parameters (4)
  • fIGM,0 = 0.935-0.999 depending on model and dataset
    Free parameter in the MCMC; in the constant case it hits the physical prior boundary f=1, with upper error truncated to 0.008.
  • alpha = 0.61-0.71 (time-dependent case)
    Evolution parameter in fIGM(z) = f0 + alpha z/(1+z); prior restricted to alpha >= 0.
  • DMhost,0 = 112-116 pc/cm3
    Global host-galaxy DM contribution, assumed identical for all FRBs after redshift scaling.
  • delta = 230*sqrt(z) pc/cm3 (fixed input)
    DM fluctuation amplitude chosen from prior literature; it dominates the error budget and affects the constraints and model comparison.
assumptions (6)
  • domain assumption Flat Universe assumed to convert DESI transverse BAO distances to luminosity distance via D_L = (1+z) D_M.
    Equations 3.3 and 3.4; the method is advertised as model-independent but flatness is assumed.
  • domain assumption Hydrogen and helium are fully ionized at z < 3, so the free-electron fraction chi(z) = 1.
    Section 2 after Eq. 2.3; incomplete reionization would change the DM_IGM integral.
  • domain assumption All host-galaxy DM is represented by one global parameter DMhost,0 scaled by 1/(1+z).
    Eq. 2.2 and the likelihood; known host DM scatter is not modeled, so it can bias fIGM.
  • domain assumption Milky Way halo DM, MW model uncertainty, and IGM DM fluctuations are fixed inputs (DMhalo=50, sigma_MW=30, delta=230 sqrt(z) pc/cm3).
    Eqs. 2.1 and 3.1; these are not derived or fitted in this paper.
  • domain assumption Prior bounds: fIGM <= 1 and alpha >= 0.
    Section 3.2; the constant-model estimate fIGM about 0.999 indicates the f=1 bound is active, and the paper does not test sensitivity to these prior bounds.
  • domain assumption External constants H0, MB, rd, and Omega_b h^2 are fixed to SH0ES and BBN values.
    Section 3.2 and Eq. 3.5; fIGM is degenerate with these inputs, so the result inherits their systematic uncertainty.

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Pith. "Pith review of Estimating the baryon fraction in the IGM from well-localized FRBs and DESI data." pith.science (2026). https://pith.science/paper/GSLA6XFO

@misc{pith2026250717693,
  author       = {Pith},
  title        = {Pith review of: Estimating the baryon fraction in the IGM from well-localized FRBs and DESI data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GSLA6XFO}},
  note         = {Machine review of arXiv:2507.17693}
}
abstract

Current measurements of Baryon Acoustic Oscillations (BAO) from the Dark Energy Spectroscopic Survey (DESI DR2), when combined with data from Type Ia supernovae (SNe), challenge the observational viability of the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model, motivating combinations of independent datasets to estimate cosmological quantities. In a previous communication, we presented a cosmological independent method to constrain the baryon fraction in the IGM ($f_{\mathrm{IGM}}$), where we derived relevant expressions for the dispersion measure ($\mathrm{DM}$) in terms of luminosity distance, allowing us to estimate $f_{\mathrm{IGM}}$ combining directly measurements of 17 well-localized FRBs and 1048 SNe from the Pantheon catalog. Here we revisit this method to constrain $f_{\mathrm{IGM}}$, considering two parameterizations for the $f_{\mathrm{IGM}}$: constant and time-dependent. We expand our sample by combining 107 well-localized Fast Radio Bursts (FRBs) with BAO measurements from DESI DR2 and SNe observations from DESY5, and the Pantheon+ catalog. We find through a Bayesian model selection analysis that a conclusive answer about the evolution of $f_{\mathrm{IGM}}$ cannot be achieved from the current FRBs observational data. In particular, our results show weak evidence in favor of the constant case.

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