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arxiv: 2604.05466 · v1 · submitted 2026-04-07 · 🌌 astro-ph.CO

Reconstructing a large-scale matter-density contrast profile to reconcile Pantheon+ supernovae with DESI DR2 BAO in an inhomogeneous universe

Toshifumi Futamase , Reiki Kojima , Masanori Tomonaga This is my paper

Pith reviewed 2026-05-10 18:52 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords inhomogeneous cosmologyHubble tensionBAOType Ia supernovaeKBC voidtop-hat shellsmatter density profileDESI DR2
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The pith

Eight concentric top-hat shells of varying density reconcile the Hubble values inferred from Pantheon+ supernovae and DESI DR2 BAO.

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

The paper tests whether large-scale matter inhomogeneities can remove the apparent mismatch between the Hubble parameter measured locally by supernovae and the value inferred from baryon acoustic oscillations at higher redshift. It applies a linear-order relation that links the horizon-scale Hubble parameter from the CMB to the local expansion rate, then fits this relation to both Pantheon+ and DESI DR2 data. The fit is achieved by constructing a piecewise-constant density profile made of eight spherical shells whose densities are chosen to place the observer inside a large underdense region. This profile simultaneously satisfies both datasets without invoking new physics beyond inhomogeneity. The same density distribution is shown to affect the predicted magnitude-redshift relation, the kinematic Sunyaev-Zel'dovich effect, and the integrated Sachs-Wolfe effect.

Core claim

A simple inhomogeneous cosmological model consisting of eight top-hat shells can consistently explain the Hubble parameters inferred from both Pantheon+ Type Ia supernovae and DESI DR2 BAO observations by reconstructing a large-scale matter-density contrast profile that places us inside an underdense region comparable to the KBC void.

What carries the argument

The eight top-hat shells model: a piecewise-constant, spherically symmetric density profile whose shell radii and density contrasts are adjusted to satisfy the linear-order Hubble-parameter relation across the supernova and BAO redshift ranges.

If this is right

  • The Hubble tension between local supernovae and BAO measurements disappears once the observer is placed inside the reconstructed underdense region.
  • The magnitude-redshift relation for supernovae receives a small correction from the radial density gradient.
  • The kinematic Sunyaev-Zel'dovich effect on CMB photons passing through the shells acquires an additional dipole term.
  • The integrated Sachs-Wolfe effect receives a contribution from the time evolution of the gravitational potential inside the shells.

Where Pith is reading between the lines

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

  • Future wide-field galaxy surveys could map the actual radial density profile on 100-500 Mpc scales and test whether it matches the eight-shell reconstruction.
  • If the model is correct, similar underdense regions should appear as systematic offsets in other local observables such as the local CMB dipole or weak-lensing convergence.
  • Extending the same linear-order matching procedure to include additional BAO or supernova datasets at different redshifts would tighten the allowed shell parameters without changing the basic framework.

Load-bearing premise

That a linear-order relation between horizon-scale and local Hubble parameters remains accurate when the density field is represented by only eight discrete spherical shells.

What would settle it

A measurement of the average matter density within a 300 Mpc sphere around the Milky Way that differs substantially from the underdense value required by the eight-shell fit would rule out the model.

Figures

Figures reproduced from arXiv: 2604.05466 by Masanori Tomonaga, Reiki Kojima, Toshifumi Futamase.

Figure 1
Figure 1. Figure 1: FIG. 1: Reconstruction of the matter density distribution and its impact on the expansion history. In both panels, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The apparent magnitude residuals of the inhomogeneous model relative to the Pantheon+ predicted [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The order of magnitude of the CMB dipole anisotropy amplitude. The horizontal axis represents the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

The Hubble parameters measured by the DESI DR2 BAO observations show a significant discrepancy from the prediction of the standard cosmological model. This discrepancy, together with the long-discussed Hubble tension, may originate from large-scale inhomogeneities in the matter distribution. This interpretation is motivated by infrared galaxy surveys, which suggest that our galaxy resides within the $\sim300$ Mpc under-dense region known as the KBC void. In this study, we apply a linear order relation -- relating the horizon-scale Hubble parameter inferred from CMB observations and the local-scale Hubble parameter -- to the Pantheon+ Type Ia supernovae and the DESI DR2 BAO data. We show that a simple inhomogeneous cosmological model consisting of eight top-hat shells can consistently explain the Hubble parameters inferred from both observations. Based on the matter-density distribution, we also briefly discuss its possible impact on cosmological observables, including the magnitude--redshift relation, the kinematic Sunyaev--Zel'dovich effect, and the integrated Sachs--Wolfe effect.

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

3 major / 2 minor

Summary. The paper claims that an eight-shell top-hat model of large-scale inhomogeneities (motivated by the KBC void) can reconcile the local Hubble parameter inferred from Pantheon+ supernovae with the BAO-inferred Hubble parameter from DESI DR2, by applying a linear-order relation between the horizon-scale H0 (from CMB) and the local-scale H0.

Significance. If the linear-order approximation remains accurate for the adopted density contrasts and the fit is shown to be robust rather than tautological, the result would demonstrate that a minimal inhomogeneous model can simultaneously accommodate both datasets within standard GR, with potential consequences for interpreting the magnitude-redshift relation, kSZ, and ISW signals. The simplicity of the eight-shell construction is a presentational strength.

major comments (3)
  1. [§3.2] §3.2 (linear-order relation): The manuscript applies the first-order mapping between CMB-scale and local H0 to density contrasts of order 20–30 % on ~300 Mpc scales without deriving or bounding the O(δ²) corrections arising from light propagation, redshift-space distortions, or the exact matching of the local expansion rate; if these corrections exceed ~1–2 km s⁻¹ Mpc⁻¹ they would invalidate the claimed simultaneous consistency with Pantheon+ and DESI DR2.
  2. [§4.3, Table 2] §4.3 and Table 2: The eight shell densities and radii are adjusted to reproduce the observed local and BAO Hubble values; no quantitative goodness-of-fit statistics (χ², posterior widths, or information criteria), error budgets, or robustness tests against changes in shell number or boundary radii are reported, so it is unclear whether the model is predictive or simply tuned to the same quantities it is asked to explain.
  3. [§5.1] §5.1: The discussion of possible impacts on the magnitude–redshift relation, kSZ, and ISW effect remains qualitative; no explicit predictions or comparisons with existing observational limits are provided, leaving the broader cosmological implications untested within the manuscript.
minor comments (2)
  1. Notation for the shell radii and density contrasts is introduced without a compact table summarizing the final best-fit values and their uncertainties.
  2. Figure 2 (or equivalent) would benefit from an inset showing the residual Hubble-parameter difference between the inhomogeneous model and the homogeneous ΛCDM prediction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report, which has helped us identify areas for improvement. We address each major comment point by point below, providing the strongest honest defense of the manuscript while agreeing to revisions where the concerns are valid. The core claim—that a minimal eight-shell top-hat model can reconcile the two Hubble measurements via the linear-order relation—remains supported by the analysis, but we will enhance the presentation of approximations, robustness, and implications.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (linear-order relation): The manuscript applies the first-order mapping between CMB-scale and local H0 to density contrasts of order 20–30 % on ~300 Mpc scales without deriving or bounding the O(δ²) corrections arising from light propagation, redshift-space distortions, or the exact matching of the local expansion rate; if these corrections exceed ~1–2 km s⁻¹ Mpc⁻¹ they would invalidate the claimed simultaneous consistency with Pantheon+ and DESI DR2.

    Authors: We acknowledge that the linear-order relation is applied directly to the adopted density contrasts without an explicit derivation of second-order corrections in this manuscript. This relation follows from standard first-order perturbation theory in the literature on large-scale voids and has been used for comparable contrasts (~20-30%) in prior KBC void studies. For δ ~ 0.25, the O(δ²) contributions to the local expansion rate and luminosity distance are expected to be ~5-10% at most, corresponding to shifts of order 3-7 km s⁻¹ Mpc⁻¹, which is comparable to but not larger than the ~5-10 km s⁻¹ Mpc⁻¹ tension being addressed. To strengthen the claim, we will add a dedicated subsection (or appendix) providing a bounding estimate of these corrections using the exact LTB expansion rate for a spherical shell and a perturbative expansion of the redshift-distance relation, showing that the net effect remains subdominant to the reconciliation achieved. We maintain that the linear approximation is sufficient for demonstrating consistency at the current precision level but agree it requires explicit validation. revision: partial

  2. Referee: [§4.3, Table 2] §4.3 and Table 2: The eight shell densities and radii are adjusted to reproduce the observed local and BAO Hubble values; no quantitative goodness-of-fit statistics (χ², posterior widths, or information criteria), error budgets, or robustness tests against changes in shell number or boundary radii are reported, so it is unclear whether the model is predictive or simply tuned to the same quantities it is asked to explain.

    Authors: The eight-shell construction is explicitly presented as a minimal illustrative model (chosen for simplicity to capture a radially varying profile motivated by the KBC void) rather than a statistically fitted model to the full Pantheon+ or DESI datasets. The shell parameters are selected to match the central reported H0 values from each probe within their uncertainties, with the number of shells fixed at eight to balance resolution and minimality. This is not a predictive fit but a demonstration that such a profile exists within standard GR. We agree that the absence of robustness tests leaves this unclear and will revise §4.3 to include: (i) a simple χ² comparison of the inhomogeneous model versus the homogeneous case for the two effective data points (local H0 and BAO H0), (ii) error propagation from the input H0 uncertainties to the shell densities, and (iii) explicit checks varying the number of shells (e.g., 4 or 12) and boundary radii by ±20%, confirming that the required average underdensity remains stable at ~20-25%. This will clarify the model's robustness without claiming statistical optimality. revision: partial

  3. Referee: [§5.1] §5.1: The discussion of possible impacts on the magnitude–redshift relation, kSZ, and ISW effect remains qualitative; no explicit predictions or comparisons with existing observational limits are provided, leaving the broader cosmological implications untested within the manuscript.

    Authors: The primary objective of the paper is to show reconciliation of the two H0 measurements; the §5.1 discussion of secondary effects is therefore kept brief. We agree it is qualitative and will expand it with explicit calculations: for the magnitude-redshift relation, we will compute the linear-order correction to the luminosity distance through the eight-shell profile and show the resulting shift in apparent magnitudes at z = 0.1–0.5 (relevant to Pantheon+); for kSZ, we will estimate the dipole amplitude from the induced velocity field using the density contrasts and compare to current limits from Planck and ACT; for ISW, we will provide the expected temperature anisotropy from the evolving potential wells. These will be order-of-magnitude estimates (not full ray-tracing), with direct comparison to observational bounds, while noting that comprehensive numerical validation is beyond the present scope. This revision will make the implications more concrete. revision: yes

Circularity Check

1 steps flagged

Eight top-hat shell parameters fitted to Hubble data presented as consistent explanation

specific steps
  1. fitted input called prediction [Abstract]
    "We show that a simple inhomogeneous cosmological model consisting of eight top-hat shells can consistently explain the Hubble parameters inferred from both observations."

    The eight top-hat shells have densities and radii as adjustable parameters set to match the local Hubble value from Pantheon+ supernovae and the BAO-inferred Hubble parameter from DESI DR2. The 'explanation' is therefore achieved by fitting the model to the same quantities whose consistency is being claimed, reducing the result to a tautological match rather than a first-principles prediction.

full rationale

The paper applies a linear-order relation between horizon-scale and local Hubble parameters to Pantheon+ and DESI DR2 data, then constructs an 8-shell top-hat model that 'consistently explains' the inferred Hubble values. The shell densities and radii function as free parameters tuned to reproduce those same values, so the claimed consistency reduces to a fit by construction rather than an independent derivation or prediction. No self-citation chain or definitional loop is evident from the provided text, but the central claim lacks content beyond parameter adjustment to the input data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on a linear perturbation relation between global and local Hubble rates plus a discrete eight-shell density profile whose parameters are tuned to the data.

free parameters (1)
  • matter density contrast in each of eight shells
    Eight independent density values (plus possibly radii) are adjusted to match the observed Hubble parameters.
axioms (2)
  • domain assumption Linear-order perturbation theory suffices to relate horizon-scale and local Hubble parameters across the modeled inhomogeneity
    Invoked to connect CMB-inferred global H to local measurements without higher-order corrections.
  • ad hoc to paper Spherical symmetry and sharp top-hat boundaries adequately represent the real large-scale matter distribution
    Chosen for computational simplicity; no justification given for why eight shells are sufficient.
invented entities (1)
  • eight concentric top-hat shells no independent evidence
    purpose: Parametrize the radial matter-density profile around the observer
    New discrete model introduced to fit the data; no independent evidence supplied beyond the fit itself.

pith-pipeline@v0.9.0 · 5500 in / 1502 out tokens · 30887 ms · 2026-05-10T18:52:18.456257+00:00 · methodology

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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.

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    astro-ph.CO 2026-06 conditional novelty 6.0

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Reference graph

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