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arxiv: 2504.06831 · v3 · submitted 2025-04-09 · 🌌 astro-ph.CO

Hubble tension and small-scale inhomogeneities on light propagation

Lucila Kraiselburd , Cassio Pigozzo , Susana J. Landau , Jailson Alcaniz This is my paper

Pith reviewed 2026-05-22 20:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Hubble tensionZKDR approximationsmall-scale inhomogeneitiesType Ia supernovaegravitational lensingPantheon+ compilationLambdaCDM modellight propagation
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The pith

The ZKDR approximation for small-scale inhomogeneities does not resolve the Hubble tension.

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

The paper tests whether relaxing the FLRW distance-redshift relation and modeling the effects of small-scale inhomogeneities via the ZKDR approximation can reconcile the discrepancy between local and CMB-based Hubble constant values. Two formulations of the ZKDR equation are applied to Pantheon+ Type Ia supernovae data and six H0LiCOW gravitational lens systems to derive constraints on cosmological and model parameters. Model comparison criteria indicate that LambdaCDM is weakly preferred over the flat ZKDR model, while the other inhomogeneous variants are strongly disfavored. The analysis concludes that ZKDR-based background models do not solve or alleviate the tension.

Core claim

A background model characterized by the ZKDR approximation and its modifications does not solve or alleviate the Hubble tension. Constraints obtained from recent Type Ia supernovae and gravitational lens data show weak preference for LambdaCDM over the flat ZKDR model, with the remaining models strongly disfavored.

What carries the argument

The Zeldovich-Kantowski-Dyer-Roeder (ZKDR) approximation, which modifies the distance-redshift relation to capture the cumulative effect of small-scale inhomogeneities on light propagation.

If this is right

  • The data show weak preference of LambdaCDM over the flat ZKDR model.
  • The remaining ZKDR models studied are strongly disfavored.
  • Cosmological parameters can still be constrained within the inhomogeneous models but the Hubble tension persists.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If ZKDR is a faithful description, then small-scale structure alone cannot account for the tension and other explanations must be considered.
  • Future distance measurements with higher precision could tighten constraints on the ZKDR parameters further.
  • Direct comparison of ZKDR predictions against N-body light-cone simulations would test the approximation's accuracy beyond current data.

Load-bearing premise

The ZKDR approximation and its two formulations accurately describe the cumulative effect of small-scale inhomogeneities on light propagation without requiring full ray-tracing in a clumpy metric.

What would settle it

A full ray-tracing calculation in a simulated clumpy universe that produces distance-redshift relations differing substantially from those of the ZKDR equation would undermine the modeling approach used to test the tension.

Figures

Figures reproduced from arXiv: 2504.06831 by Cassio Pigozzo, Jailson Alcaniz, Lucila Kraiselburd, Susana J. Landau.

Figure 1
Figure 1. Figure 1: Results of the statistical analyses assuming a flat universe and constant [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results of the statistical analyses assuming a flat universe and constant [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The same as in previous figure for non-flat geometries. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Context. A major observational challenge within the standard cosmological framework is the Hubble tension, a statistically significant ($\sim 5\sigma$) disagreement between the Hubble constant derived from cosmic microwave background measurements and the value obtained through local distance-ladder methods based on Type Ia supernovae and Cepheid variable stars. Aims. We relax the assumption of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) distance-redshift relation and explore the influence of small-scale inhomogeneities on the propagation of light from distant sources, using the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) approximation as an alternative approach to address this tension. Methods. We employ two distinct formulations of the ZKDR equation to test our hypothesis using recent Type Ia supernovae datafrom the Pantheon+ compilation and the SH0ES collaboration and six gravitational lens systems from the H0LiCOW collaboration. Results. We obtained constraints on the cosmological parameters and the ZKDR model parameters within the framework of the inhomogeneous models considered. The model comparison criterion indicates that the data show weak preference of $\Lambda$CDM over the flat ZKDR model , whereas the remaining models studied are strongly disfavored. Conclusions. Our findings indicate that a background model characterized by the ZKDR approximation and its modifications does not solve or alleviate the Hubble tension.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript tests whether the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) approximation and two of its variants can resolve the Hubble tension by altering the distance-redshift relation due to small-scale inhomogeneities. The authors fit the models to Pantheon+ Type Ia supernovae (combined with SH0ES) and six H0LiCOW gravitational lens systems, obtain constraints on cosmological and inhomogeneity parameters, and use information criteria to compare models. They conclude that these inhomogeneous models do not solve or alleviate the tension, with ΛCDM weakly preferred over the flat ZKDR model and the other variants strongly disfavored.

Significance. If the ZKDR approximation and its variants correctly capture the net effect of inhomogeneities on light propagation for the relevant redshifts and without significant omitted backreaction or selection biases, the result would strengthen the case that adjustments to the distance-redshift relation alone via this averaging approach are insufficient to reconcile local H0 measurements with CMB-inferred values. The concrete use of Pantheon+ and H0LiCOW datasets provides a direct, falsifiable test of one proposed resolution mechanism.

major comments (2)
  1. [Methods] Methods section: the manuscript does not provide an explicit check that the averaging scale implicit in the ZKDR inhomogeneity parameter matches the redshift range spanned by the Pantheon+ supernovae and H0LiCOW lenses. Without this, it is unclear whether the fitted clumpiness parameter is being applied in a regime where the approximation is valid.
  2. [§2] §2 and likelihood description: the uncertainty on the ZKDR clumpiness parameter is not shown to be propagated through the joint likelihood that includes the SH0ES calibration; this risks underestimating the posterior width on H0 and weakening the claim that the tension remains unresolved.
minor comments (2)
  1. [Abstract / Methods] The abstract states that Pantheon+ data are combined with SH0ES, yet the precise form of the joint likelihood (e.g., how the Cepheid calibration enters) is not summarized in the methods overview.
  2. [Figures/Tables] Figure captions and table headers should explicitly state the priors adopted for the ZKDR inhomogeneity parameters to allow immediate assessment of the model comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. The points raised concern the applicability of the ZKDR approximation and the presentation of uncertainty propagation in our joint analysis. We address each major comment below and will incorporate revisions to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Methods] Methods section: the manuscript does not provide an explicit check that the averaging scale implicit in the ZKDR inhomogeneity parameter matches the redshift range spanned by the Pantheon+ supernovae and H0LiCOW lenses. Without this, it is unclear whether the fitted clumpiness parameter is being applied in a regime where the approximation is valid.

    Authors: We agree that an explicit discussion of the averaging scale would strengthen the manuscript. The ZKDR approximation is typically valid for inhomogeneity scales much smaller than the horizon but larger than individual galaxies or clusters, and the redshifts of Pantheon+ (0.001 < z < 2.26) and H0LiCOW lenses (z ≈ 0.3–1.0) fall within ranges previously studied with this approach. We will add a paragraph to the Methods section referencing the derivation of the averaging scale and confirming its applicability to these datasets, including citations to prior validations. revision: yes

  2. Referee: [§2] §2 and likelihood description: the uncertainty on the ZKDR clumpiness parameter is not shown to be propagated through the joint likelihood that includes the SH0ES calibration; this risks underestimating the posterior width on H0 and weakening the claim that the tension remains unresolved.

    Authors: We acknowledge that the manuscript should more explicitly demonstrate the propagation of the clumpiness parameter uncertainty. The parameter is treated as a free parameter with its prior and is jointly sampled with H0 and other parameters in the full likelihood that incorporates SH0ES data. However, the presentation does not clearly illustrate this marginalization. We will revise §2 to include a detailed description of the joint posterior sampling and add a note or supplementary figure confirming that the reported H0 uncertainties account for the clumpiness parameter variance. This will not alter our conclusion that the tension is unresolved. revision: yes

Circularity Check

0 steps flagged

No significant circularity in ZKDR fitting and model comparison

full rationale

The paper fits the parameters of two ZKDR formulations to Pantheon+ supernova and H0LiCOW lens data, then applies standard information criteria for model comparison against LCDM. The central claim that these models do not alleviate the Hubble tension follows from the resulting posterior constraints and Bayes factors without any step reducing the output to the input by construction, self-definition, or load-bearing self-citation. The ZKDR equation itself is treated as an external approximation whose validity is an assumption, not derived within the paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the validity of the ZKDR approximation as a proxy for inhomogeneity effects and on the assumption that the chosen data sets are free of unmodeled systematics that could mimic or mask the tension.

free parameters (1)
  • ZKDR inhomogeneity parameters
    Parameters controlling the degree of clumpiness in the two ZKDR formulations are fitted to the supernova and lens data.
axioms (1)
  • domain assumption ZKDR approximation accurately models light propagation through small-scale inhomogeneities
    Invoked to relax the FLRW distance-redshift relation as an alternative to standard cosmology.

pith-pipeline@v0.9.0 · 5785 in / 1219 out tokens · 43715 ms · 2026-05-22T20:48:58.683890+00:00 · methodology

discussion (0)

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Reference graph

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