Cosmological-model independent limits on photon mass from FRB and SNe data

Jailson Alcaniz; Joel Carvalho; Rodrigo Gon\c{c}alves; Thais Lemos

REVIEW 3 major objections 5 minor 1 cited by

Cosmological-model independent limits on photon mass from FRB and SNe data

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper shows that photon rest mass can be constrained without assuming a cosmological model, by using fast radio burst dispersion measures together with supernova distances.

desk verdict Honest, incremental extension of the authors' own model-independent FRB+SNe method to photon mass, with an unstated flatness assumption behind Eq. 4.6 that is real but numerically minor; the paper deserves a serious referee. read the letter →

arxiv 2504.21129 v1 pith:27YZUPQJ submitted 2025-04-29 astro-ph.CO astro-ph.HEhep-ph

Thais Lemos , Rodrigo Gonçalves , Joel Carvalho , Jailson Alcaniz This is my paper · ORCID

classification astro-ph.COastro-ph.HEhep-ph

keywords photonrestmassfastradioburstsdispersionmeasuretypeIasupernovaeintergalacticmediummodel-independentcosmologyPantheonbaryonfraction

open problems Dark Energy

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 bound the rest mass of the photon without committing to a cosmological model. It combines the dispersion measures of 68 well-localized fast radio bursts with luminosity distances of 1048 type Ia supernovae from the Pantheon catalog, rewriting both the intergalactic-medium and the massive-photon dispersion integrals as functions of the supernova luminosity distance. In the case where the IGM baryon fraction is treated as free, the photon mass is found to be $m_\gamma = (29.4^{+5.8}_{-15.5}) \times 10^{-51}$ kg at $1\sigma$, with $f_{\mathrm{IGM,0}} = 0.902^{+0.034}_{-0.631}$. The result is consistent with a zero photon mass at about $2\sigma$, and it shows a strong anticorrelation between $m_\gamma$ and $f_{\mathrm{IGM}}$, which the authors read as a warning that baryon-fraction assumptions dominate the constraint.

What carries the argument

The central object is the decomposition of the observed extragalactic dispersion measure into host, IGM, and photon-mass terms, $\mathrm{DM}_{\mathrm{ext}}^{\mathrm{th}}(z) = \mathrm{DM}_{\mathrm{host}}(z) + \mathrm{DM}_{\mathrm{IGM}}(z) + \mathrm{DM}_\gamma(z)$. The load-bearing move is the integration-by-parts identities $$\mathrm{DM}_{\mathrm{IGM}}(z) = A\,f_{\mathrm{IGM,0}}\left[ \frac{d_L(z)}{c} - \frac{1}{c}\int_0^z \frac{d_L(z')}{1+z'}\,dz' \right]$$ and the displayed expression for $\mathrm{DM}_\gamma(z)$, which convert the unknown Hubble-parameter integrals into luminosity distances that the Pantheon SNe supply through a Gaussian-process reconstruction. All the cosmology is thereby concentrated in $d_L(z)$, so the comparison of theory to the measured DM of 68 FRBs constrains $m_\gamma$, $f_{\mathrm{IGM,0}}$, and $\mathrm{DM}_{\mathrm{host,0}}$ without specifying a dark-energy model.

What would settle it

A single well-localized FRB with an independently measured luminosity distance (for example from a gravitational-wave standard siren or a Cepheid-calibrated host) would settle the flatness question: if the DM_IGM and DM_gamma residuals computed with the true d_L disagree with the fitted m_gamma at more than the quoted 1-sigma level, the massive-photon interpretation fails. More directly, a future sample of hundreds of FRBs should show residuals around the model that are statistically consistent with the fitted m_gamma; a significant excess that correlates with redshift and not with host properties would falsify the model.

Watch

Extended reading notes

Core claim

The paper's central claim is that the photon rest mass can be constrained from FRB dispersion measures without assuming $\Lambda$CDM by expressing the massive-photon contribution as $$\mathrm{DM}_\gamma(z) = B\,m_\$gamma^{2}$\left[ \frac{d_L(z)}{(1+z)^3} + \frac{2}{c}\int_0^z \frac{d_L(z')}{(1+z')^4}\,dz' \right],$$ where $d_L$ comes directly from SNe data. This expression follows from integration by parts on the massive-photon dispersion integral using the luminosity-distance relation, avoiding the Hubble-parameter integrals that would require a cosmological model. With 68 well-localized FRBs and Pantheon SNe, the analysis yields $m_\gamma = (29.4^{+5.8}_{-15.5}) \times 10^{-51}$ kg ($1\sigma$) when $f_{\mathrm{IGM}}$ is free, and $m_\gamma = (18.2^{+2.7}_{-5.9}) \times 10^{-51}$ kg when $f_{\mathrm{IGM}} = 0.83$ is fixed; the host-galaxy term is constrained to around 90--100 pc/cm$^3$. The paper also claims a tight anticorrelation between $m_\gamma$ and $f_{\mathrm{IGM,0}}$.

Load-bearing premise

The derivation rests on the flat-universe relation between luminosity distance and expansion rate, $d_L(z) = (1+z)c\int_0^z dz'/H(z')$, which the paper does not state explicitly; if spatial curvature is nonzero, the dispersion-measure terms acquire extra geometric factors and the inferred photon mass shifts.

Editorial extensions

If this is right

If the free-$f_{\mathrm{IGM}}$ result is right, the photon rest mass is not zero at the roughly $2\sigma$ level, with a central value around $3\times10^{-50}$ kg, a factor of several above the previous model-independent limit from 32 FRBs ($m_\gamma \le 3.5\times10^{-51}$ kg).
The strong anticorrelation between $m_\gamma$ and $f_{\mathrm{IGM,0}}$ means that any assumed baryon fraction directly biases the inferred photon mass; fixing $f_{\mathrm{IGM,0}}$ can move the central value by roughly $11\times10^{-51}$ kg.
The host-galaxy dispersion measure is constrained to $\mathrm{DM}_{\mathrm{host,0}} \sim 90$--$100$ pc/cm$^3$, consistent with current FRB host-galaxy modeling.
The method is agnostic to the expansion history, so it can be applied as the sample of well-localized FRBs grows without needing to revisit the cosmological model.

Reading between the lines

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

Going beyond the paper, the unstated flat-geometry assumption may be the weakest link: the luminosity-distance identities used in Eqs. (4.5)--(4.6) rely on $d_L(z) = (1+z)c\int_0^z dz'/H(z')$, which holds only for zero spatial curvature; a non-flat universe would introduce extra geometric factors and shift the inferred $m_\gamma$.
A direct testable extension would measure the frequency-dependent arrival-time residual within individual FRBs (or among sub-bursts) and compare the implied $m_\gamma$ with the ensemble value; a mismatch would expose the ensemble modeling of $\mathrm{DM}_{\mathrm{host}}$ and $f_{\mathrm{IGM}}$.
The same integration-by-parts machinery could be applied to other frequency-dependent propagation effects, such as axion-photon mixing or Lorentz-invariance violation, replacing $m_\gamma$ with the relevant coupling.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know two things. This is the same group's model-independent FRB+SNe machinery, now pointed at the photon mass; the new pieces are the luminosity-distance form of the massive-photon DM integral (Eq. 4.6) and a constraint from 68 FRBs plus Pantheon. The result is modest: the free-f_IGM case gives m_γ = (29.4^{+5.8}_{-15.5})×10^{-51} kg at 1σ, consistent with zero at ~2σ, and about ten times weaker than the existing cosmology-independent limit from Ran, Wang & Wei (≤3.5×10^{-51} kg). That is stated plainly.

The authors do a lot right. The data cuts are itemized with reasons, the f_IGM–m_γ degeneracy is acknowledged and displayed, and there is no detection overclaim. The method does avoid the ΛCDM circularity it criticizes: the photon mass is fitted, not assumed. The citation pattern is healthy—closely related work is cited and compared, and the self-reference to [27] is legitimate since this is their own machinery.

Soft spots, in order of how much they matter. The flatness assumption: the stress-test is right that Eqs. 4.5–4.6 use d_L = (1+z)c∫dz/H, the flat-FLRW identity, and the paper never says so. The practical bias is small—with |Ω_k| ≲ 0.02 the curvature correction is of order Ω_k (∫_0^z H_0/H dz')^2/6, around 10^{-3}—so it will not change the answer, but the label 'cosmological-model independent' should be qualified to 'flat', and a sentence plus a curvature robustness run would settle it.

Then three smaller things. Eq. 4.6 as printed has a units problem in the first term: it should be d_L/(c(1+z)^3) to match the (2/c)∫ term; likely a typo, but it needs fixing. Eq. 4.5 drops the χ = 7/8 factor that Eq. 3.14 defines; the fitted f_IGM,0 then absorbs that factor, which changes the comparison with external baryon-fraction estimates and can shift the fixed-case m_γ by ~10%. And the MCMC priors are not reported, while H0 and Ω_b enter with quoted errors that are not marginalized over; the first is a reproducibility issue, the second is an easy improvement.

The single global DM_host,0 for all 68 FRBs is crude, and the pruning from 97 to 68 events is justified but deserves a robustness check. The fixed-f_IGM case actually excludes m_γ = 0 at ~3σ; given the missing 7/8 factor, that tension should be examined before anyone quotes it as a hint.

Bottom line: a publishable-after-revision paper, not a breakthrough. It advances the program incrementally, is honestly presented, and the central method survives the flatness critique numerically. If you work on FRB dispersion or photon-mass bounds, it is worth a read as a cross-check; if not, it can wait. It deserves a serious referee—the derivation issue is real but fixable, and the transparency makes referee work tractable. My recommendation: send it to peer review, and ask for the flatness statement, the two equation fixes, and the robustness checks.

Referee Report

3 major / 5 minor

Summary. This paper constrains the photon rest mass mγ by combining 68 well-localized fast radio bursts with luminosity distances reconstructed from the 1048-object Pantheon supernova sample. Starting from the massive-photon dispersion relation, the authors define a photon-mass contribution DMγ(z) to the dispersion measure and rewrite both DM_IGM and DM_γ in Eqs. (4.5)–(4.6) as combinations of the luminosity distance and redshift integrals, avoiding any assumed H(z). An MCMC is then run for two scenarios: f_IGM fixed at 0.83 and f_IGM free. The free case yields mγ = (29.4^{+5.8}_{−15.5}) × 10^{-51} kg, f_IGM,0 = 0.902^{+0.034}_{−0.631}, and DM_host,0 = 90^{+19}_{−22} pc/cm^3 at 1σ, together with a strong anticorrelation between f_IGM and mγ. The fixed case gives mγ = (18.2^{+2.7}_{−5.9}) × 10^{-51} kg.

Significance. The intended contribution is a photon-mass limit that avoids specifying the dark-energy expansion history and therefore avoids the ΛCDM circularity present in earlier FRB-based limits. The paper's algebraic transformation of the DM integrals into d_L-based terms is transparent and, under a flat FLRW geometry, internally consistent. It also makes efficient use of the growing sample of localized FRBs and tabulates the individual events. The main limitation is that the 'cosmological-model independent' phrasing overstates the result: the key identities assume flat spatial geometry, and the error budget omits some external uncertainties. With these points addressed, the method is a useful and falsifiable approach to photon-mass constraints.

major comments (3)

[§4.3, Eqs. (4.5)–(4.6)] The derivation of DM_IGM and DM_γ is done by integration by parts using the flat-FLRW relation d_L(z) = (1+z)c∫_0^z dz'/H(z'). For nonvanishing spatial curvature, d_L/(1+z) is the transverse comoving distance D_M(z) = S_k(χ), whose derivative is not c/H, so the identities in Eqs. (4.5) and (4.6) acquire Ω_k-dependent correction factors. The paper never states that flatness is assumed. This matters because DMγ enters as mγ² and is degenerate with f_IGM,0 and DM_host,0 through Eq. (3.12), so a curvature correction shifts the inferred mγ and its uncertainty. Please state the flatness assumption explicitly, or generalize the derivation to S_k, or quantify the sensitivity to Ω_k; as written, the 'cosmological-model independent' claim rests on an unstated geometric premise.
[§4.3, Eqs. (4.1)–(4.2)] The quoted external uncertainties H0 = 74.03 ± 1.4 km/s/Mpc and Ω_b h² = 0.02235 ± 0.00037 are not propagated into σ_IGM or into the MCMC likelihood. The prefactor A = 3cΩ_b H0²/(8πG m_p) in Eq. (4.5) contains H0² and Ω_b, so its fractional uncertainty is roughly 4%, yet Eq. (4.2) includes only σ_dL and σ_I. Because DM_IGM is proportional to A f_IGM,0 and mγ is found to be anticorrelated with f_IGM,0, the omission can underestimate the error bars on mγ. Please propagate the H0 and Ω_b uncertainties, or show explicitly that their effect is negligible for the reported 1σ intervals.
[§4.3, Eq. (4.2)] The uncertainty σ_I of the integral in Eq. (4.6) is not defined. The integral is computed from GP-reconstructed d_L values at a set of redshifts, and those values are strongly correlated in the GP posterior. If σ_I is computed from the diagonal errors only, the likelihood overstates the information content of the data and the reported uncertainties are not reliable. Please specify how σ_I is calculated, including whether the full GP covariance matrix is propagated.

minor comments (5)

[§5, first paragraph] The phrase 'a discrepancy value between them at 11.2×10^-31 kg' should read 10^-51 kg, since the constraints are quoted in units of 10^-51 kg.
[§4.3] The likelihood function and the priors used in the emcee runs are not stated; please include the exact likelihood expression and the prior ranges or distributions for mγ, f_IGM,0, and DM_host,0 for reproducibility.
[§4.2] The Pantheon systematic covariance matrix is not used in the GP reconstruction of d_L; the authors should state whether this is intentional and whether the supernova systematics are reflected in σ_dL.
[§4.1] The fixed 30 pc/cm^3 host-galaxy uncertainty enters Eq. (4.1) in quadrature, but the treatment of the host-galaxy scatter and its relation to the fitted DM_host,0 is not discussed; a brief justification would help.
[§6] The comparison with Ref. [45] mentions sample size and number of free parameters, but not the different treatment of f_IGM; adding a sentence noting that [45] fixes f_IGM while the present work fits it would make the comparison clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: m_gamma is fitted, not presupposed; the DM_IGM/DM_gamma rewrites are algebraic identities under flat FLRW, with the flatness assumption being an unstated modeling risk rather than an input-output loop.

full rationale

The central quantity m_gamma enters only through Eq. (3.9), obtained from the massive-photon dispersion relation and the group-velocity expression, and is then constrained by MCMC against observed DMs. Equations (4.5) and (4.6) are integration-by-parts identities that rewrite DM_IGM and DM_gamma in terms of the SNe luminosity distance under d_L=(1+z)c∫dz'/H; this is a mathematical transformation, not an assignment of the target parameters. The SNe distances provide d_L as input, while DM_obs and z provide the independent data; m_gamma, f_IGM,0 and DM_host,0 are free parameters of the fit. The self-citation to [27] points to the same integration-by-parts technique, but the paper presents the relevant expressions and the technique is a parameter-free algebraic identity, so it is not load-bearing circularity. The main caveat is the unstated flat-FLRW relation used in Eqs. (4.5)-(4.6) and the external H0/MB calibration; this is a model-dependence and correctness concern, not a circularity, because the inputs do not already contain the inferred m_gamma.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The paper adds one target parameter (m_γ) and two nuisance parameters (f_IGM,0, DM_host,0), plus a hand-set halo value. The main hidden load-bearing input is the flat-universe geometric relation that enables the model-independent rewriting of the DM integrals. No new particles or fields are introduced beyond the massive photon already assumed in the Proca framework. Gaussian process hyperparameters are also optimized over the SNe data, but they are intermediate and not part of the final likelihood, so they are not listed as separate entries.

free parameters (4)

m_γ (photon rest mass) = 29.4^{+5.8}_{-15.5} × 10^{-51} kg (free case); 18.2^{+2.7}_{-5.9} × 10^{-51} kg (fixed case)
The target parameter of the analysis, fitted by MCMC to the FRB DM residuals. It is the central claim, not a nuisance, but it is a free parameter in the likelihood.
f_IGM,0 (IGM baryon fraction) = 0.902^{+0.034}_{-0.631}
Free in one scenario; in the fixed scenario set to 0.83 from Ref. [97]. Fitted because the baryon fraction in the IGM is poorly known and degenerate with m_γ.
DM_host,0 (host galaxy DM) = 90^{+19}_{-22} pc/cm^3 (free case); 100 ± 18 pc/cm^3 (fixed case)
A single global host-galaxy dispersion contribution shared by all FRBs, fitted because individual host environments are not well measured.
DM_halo (Milky Way halo DM) = 50 pc/cm^3 (fixed by hand)
Chosen value following Ref. [30]. The central m_γ shifts if this halo contribution is different, so it is a hand-set input to the model.

assumptions (8)

domain assumption Flat FLRW geometry: d_L(z) = (1+z)c ∫_0^z dz'/H(z')
Used without statement to convert DM integrals into luminosity-distance terms in Eq. 4.5 and Eq. 4.6. Fails if Ω_k ≠ 0. This is the paper's weakest assumption.
domain assumption IGM is fully ionized at z<3, χ(z)=7/8
Adopted in Section 3.2 following Ref. [55]; affects the normalization of DM_IGM.
domain assumption f_IGM is constant, with no redshift evolution
The paper restricts to the constant case because evidence for time dependence was inconclusive in their earlier work [27].
domain assumption DM_host(z) = DM_host,0/(1+z)
Standard parametrization of host-galaxy dispersion evolution, Eq. 3.13, following Refs. [49,54].
domain assumption Massive-photon (Proca) dispersion relation ω^2 = k^2c^2 + ω_p^2 + ω_γ^2
The theoretical framework for the photon-mass effect, Eq. 3.1. This is the new-physics premise being tested.
domain assumption MW halo DM fixed at 50 pc/cm^3
Assumed in Section 3.2 following Ref. [30]; uncertainty in this value is not modeled.
domain assumption Noise model σ_tot^2 includes fixed σ_MW=10 pc/cm^3, σ_host,0=30 pc/cm^3, and IGM variance δ=230√z pc/cm^3
Eq. 4.1; these hand-set uncertainties shape the reported 1σ intervals for m_γ.
domain assumption Gaussian process reconstruction of d_L from SNe distance moduli
The GP prior and kernel choice affect d_L and its uncertainty at FRB redshifts; the paper uses the GaPP library [95].

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Pith. "Pith review of Cosmological-model independent limits on photon mass from FRB and SNe data." pith.science (2026). https://pith.science/paper/27YZUPQJ

@misc{pith2026250421129,
  author       = {Pith},
  title        = {Pith review of: Cosmological-model independent limits on photon mass from FRB and SNe data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/27YZUPQJ}},
  note         = {Machine review of arXiv:2504.21129}
}

abstract

Electromagnetic emissions from astrophysical sources at cosmological distances can be used to estimate the photon mass, $m_{\gamma}$. In this paper, we combine measurements of the dispersion measure ($\mathrm{DM}$) of fast radio bursts (FRB) with the luminosity distance from type Ia supernovae (SNe) to investigate update constraints on the photon rest mass. We derive the expression of $\mathrm{DM}$ dependence concerning a non-vanishing photon mass from a cosmological-model independent approach and constrain the parameter $m_{\gamma}$ from measurements of 68 well-localized FRBs and 1048 SNe data from the Pantheon compilation. We consider two scenarios for the baryon fraction in the intergalactic medium ($f_{\mathrm{IGM}}$): one where the value is fixed according to recent reports and another where it is treated as a free parameter, $f_{\mathrm{IGM}} = f_{\mathrm{IGM,0}}$. In the latter case, we find $m_{\gamma} = (29.4_{-15.5}^{+5.80}) \times 10^{-51}$ kg, at $1\sigma$ level. Our results also demonstrate an anticorrelation between $f_{\mathrm{IGM}}$ and $m_{\gamma}$, which highlights the importance of analyzing a larger sample of FRBs for a more comprehensive understanding of their properties.

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Forward citations

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