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arxiv: 2512.02526 · v2 · submitted 2025-12-02 · 🌌 astro-ph.CO · gr-qc· hep-th

Recognition: 2 theorem links

· Lean Theorem

Updates on dipolar anisotropy in local measurements of the Hubble constant from Cosmicflows-4

Vincenzo Salzano , J. Beltr\'an Jim\'enez , Dario Bettoni , Philippe Brax , Aur\'elien Valade
Authors on Pith no claims yet

Pith reviewed 2026-05-17 02:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-th
keywords dipolar anisotropyHubble constantCosmicflows-4peculiar velocitiesdistance modulispherical harmonicsisotropic expansionHubble tension
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The pith

Peculiar-velocity corrections largely erase the observed dipole anisotropy in local Hubble constant measurements from Cosmicflows-4

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

The paper investigates angular variations in the Hubble constant by analyzing the Cosmicflows-4 catalogue through a logarithmic formulation based on distance moduli. It performs internal consistency checks to select conservative subsamples that minimize selection effects and then maps log H0 using spherical-harmonic fits up to octupole order. A clear dipole signal appears in the raw data but drops sharply once peculiar-velocity corrections are applied, especially at lower depths, with no strong evidence for radial evolution in the dipole. These findings point to local velocity flows and catalogue structure as the main drivers of the anisotropy rather than any large-scale departure from isotropic expansion, while suggesting only limited consequences for the broader Hubble tension.

Core claim

A statistically significant dipole anisotropy is present in the uncorrected Cosmicflows-4 data and is favoured over a monopole-only model by Bayesian evidence. When peculiar-velocity corrections are applied the anisotropy amplitude is strongly reduced, particularly at lower depths, while only a weaker residual signal survives at larger distances. No robust evidence is found for a monotonic radial evolution of the dipole. The results indicate that the anisotropy arises primarily from local velocity flows and catalogue or survey structure rather than a large-scale breakdown of isotropic expansion, and that any effect on global Hubble tension determinations is likely limited.

What carries the argument

Spherical-harmonic expansion up to octupole order fitted to angular maps of log H0, derived from a logarithmic Hubble-Lemaître relation based directly on distance moduli in selected radial shells.

Load-bearing premise

Peculiar-velocity corrections are assumed to remove local flow effects accurately without leaving residual biases that could create or hide apparent anisotropy.

What would settle it

A persistent dipole of comparable amplitude in the peculiar-velocity-corrected data at redshifts above 0.06 would undermine the claim that local flows and survey structure are the dominant source.

Figures

Figures reproduced from arXiv: 2512.02526 by Aur\'elien Valade, Dario Bettoni, J. Beltr\'an Jim\'enez, Philippe Brax, Vincenzo Salzano.

Figure 1
Figure 1. Figure 1: Hubble-Lemaˆıtre law from the Cosmicflows-4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Positions of the objects in the CF4obs catalog in galactic coordinates. IV. ANALYSIS In this section, we will describe the key choices and elements of our analysis in detail, from the selection of the sample and its properties to the specifics of the statistical analysis conducted. A. Building the subsample [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Hubble constant average, ⟨log H0⟩, in radial shells of width ∆µ = 0.2 and at average distance µ. Full CF4 sample, gray; v obs CMB > 4000 km s−1 , red; {|v X LS|, |v Y LS|, |v Z LS|} < 16000 km s−1 , blue; {|v X LS|, |v Y LS|, |v Z LS|} < 8000 km s−1 , cyan; {|v X LS|, |v Y LS|, |v Z LS|} < 5000 km s−1 , magenta; σµ/µ < 0.006, green. As our goal is to test for possible anisotropic signals, particular care m… view at source ↗
Figure 4
Figure 4. Figure 4: Angular distribution in galactic coordinate system of the radial shells described in Sec. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Radial+Angular radial shells in Galactic [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Radial variation of: Hubble constant (top left), the dipole coefficient, a1 (green) and of dipole-to-monopole ratio, C1/C0 (orange) (top right); bulk velocity estimated from the dipole using the CF4obs sample (bottom left) and the CF4pec (bottom right). Boxes represent the distance interval (horizontal), µ, and the error interval (vertical) on the given quantity; the black stars correspond to the estimatio… view at source ↗
Figure 7
Figure 7. Figure 7: Radial+Angular signal per radial shells in Galactic coordinate system and CMB frame for the CF4 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Radial+Angular signal per radial shells in Galactic coordinate system and CMB frame for the CF4 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Radial+Angular signal per radial shells in Galactic coordinate system and CMB frame for the CF4 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Radial+Angular signal per radial shells in Galactic coordinate system and CMB frame for the CF4 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Radial+Angular signal per radial shells in Galactic coordinate system and CMB frame for the CF4 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

We investigate the angular anisotropy of the Hubble constant using the Cosmicflows-4 catalogue, with particular emphasis on three issues often treated only implicitly in the literature: the statistical formulation of the Hubble--Lema\^{i}tre relation, the internal consistency of the working sample, and the role of peculiar-velocity corrections. Rather than working in luminosity-distance space, we adopt a logarithmic formulation based directly on distance moduli, thereby preserving the Gaussian error properties of the measured quantities. We first subject the catalogue to internal consistency tests, including the depth dependence of $\langle \log H_0 \rangle$ and the behaviour of residual skewness and kurtosis across radial shells, and use these diagnostics to define conservative subsamples minimally affected by selection effects, namely $\mu \in [31,36]$ and $z \in [0.03,0.06]$. Within these ranges, we reconstruct angular maps of $\log H_0$ and fit them with a spherical-harmonic expansion up to octupole order. We find a statistically significant anisotropic signal in the uncorrected CF4 data, dominated by a dipole and favoured over a monopole-only model by Bayesian evidence. However, when peculiar-velocity-corrected data are used, the anisotropy amplitude is strongly reduced, especially at lower depths, while only a weaker residual signal survives at larger distances. We also test for a monotonic radial evolution of the dipole, as expected in some differential-expansion scenarios, but find no robust evidence for such a trend. These results indicate that the anisotropy is driven primarily by local velocity flows and catalogue/survey structure, rather than by a large-scale breakdown of isotropic expansion. Finally, we show that although such anisotropy may affect local determinations of $H_0$, its impact on the global Hubble tension is likely limited.

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 analyzes angular anisotropy in local Hubble constant measurements from the Cosmicflows-4 catalogue. It adopts a logarithmic formulation of the Hubble-Lemaître relation using distance moduli to preserve Gaussian errors, applies internal consistency tests (depth dependence of ⟨log H0⟩ and residual skewness/kurtosis) to select conservative subsamples (μ ∈ [31,36] and z ∈ [0.03,0.06]), and fits spherical-harmonic expansions up to octupole order to angular maps of log H0. The analysis finds significant dipole-dominated anisotropy in uncorrected data that is strongly reduced after peculiar-velocity corrections, with no robust evidence for monotonic radial dipole evolution; the authors conclude that the signal arises primarily from local velocity flows and catalogue/survey structure rather than large-scale isotropy violation, and that its effect on the global Hubble tension is limited.

Significance. If the central result holds, the work strengthens the case that apparent dipolar anisotropy in local H0 determinations is attributable to peculiar velocities and selection effects rather than a breakdown of the cosmological principle. This has implications for interpreting the Hubble tension, as it suggests local measurements can be reconciled with isotropic expansion once local flows are properly modeled. The use of public catalogue data, internal diagnostics for subsample selection, and Bayesian model comparison are positive features that enhance reproducibility and falsifiability.

major comments (3)
  1. [Section on peculiar-velocity corrections and subsample definition] The reduction in dipole amplitude after peculiar-velocity corrections (central to the claim that anisotropy is driven by local flows) relies on the assumption that these corrections remove only true velocity contributions without introducing or suppressing angular structure correlated with the CF4 selection function. However, the internal consistency diagnostics used to define the μ ∈ [31,36] and z ∈ [0.03,0.06] subsamples are applied alongside or after the same corrections, creating potential non-independence; a quantitative test of residual angular correlations (e.g., via mock catalogues with known velocity fields) would be needed to confirm the evidence is independent.
  2. [Section on spherical-harmonic expansion and model comparison] The spherical-harmonic fits and Bayesian evidence comparison between anisotropic (dipole+monopole) and isotropic (monopole-only) models are load-bearing for the main conclusion, yet details on error propagation, exact likelihood formulation, and priors are not fully specified; this is particularly relevant for the reported loss of Bayesian preference after corrections and for the weaker residual signal at larger distances.
  3. [Section on radial dipole evolution test] The test for monotonic radial evolution of the dipole (expected in some differential-expansion scenarios) finds no robust evidence, but the chosen z ∈ [0.03,0.06] range is narrow; extending the analysis to a broader depth baseline or explicitly comparing against predicted trends from specific models would strengthen the rejection of large-scale alternatives.
minor comments (2)
  1. [Introduction and methods] Notation for the logarithmic Hubble constant (log H0) and distance modulus μ should be defined explicitly at first use, and consistency with standard conventions in the literature checked.
  2. [Results figures] Figure captions for the angular maps and residual plots would benefit from explicit mention of the survey mask, depth shells, and any applied weighting to aid interpretation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify and strengthen our analysis of the angular anisotropy in the Cosmicflows-4 data. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Section on peculiar-velocity corrections and subsample definition] The reduction in dipole amplitude after peculiar-velocity corrections (central to the claim that anisotropy is driven by local flows) relies on the assumption that these corrections remove only true velocity contributions without introducing or suppressing angular structure correlated with the CF4 selection function. However, the internal consistency diagnostics used to define the μ ∈ [31,36] and z ∈ [0.03,0.06] subsamples are applied alongside or after the same corrections, creating potential non-independence; a quantitative test of residual angular correlations (e.g., via mock catalogues with known velocity fields) would be needed to confirm the evidence is independent.

    Authors: We thank the referee for this important observation on potential non-independence. The internal consistency tests for subsample selection (depth dependence of ⟨log H0⟩ and residual skewness/kurtosis) were performed on the uncorrected data prior to applying peculiar-velocity corrections. Nevertheless, to directly address concerns about residual angular correlations with the selection function, we will add a quantitative validation using mock catalogues that incorporate known velocity fields and the CF4 selection function. This will confirm that the dipole reduction is attributable to the removal of true peculiar velocities rather than an artifact of the corrections. revision: yes

  2. Referee: [Section on spherical-harmonic expansion and model comparison] The spherical-harmonic fits and Bayesian evidence comparison between anisotropic (dipole+monopole) and isotropic (monopole-only) models are load-bearing for the main conclusion, yet details on error propagation, exact likelihood formulation, and priors are not fully specified; this is particularly relevant for the reported loss of Bayesian preference after corrections and for the weaker residual signal at larger distances.

    Authors: We agree that fuller specification of the statistical details is warranted for reproducibility. In the revised manuscript we will expand the relevant sections to include explicit descriptions of error propagation through the logarithmic Hubble-Lemaître relation, the precise likelihood function employed in the spherical-harmonic fits, and the priors used for the Bayesian evidence comparison. These additions will clarify the robustness of the reported loss of preference for the anisotropic model after corrections. revision: yes

  3. Referee: [Section on radial dipole evolution test] The test for monotonic radial evolution of the dipole (expected in some differential-expansion scenarios) finds no robust evidence, but the chosen z ∈ [0.03,0.06] range is narrow; extending the analysis to a broader depth baseline or explicitly comparing against predicted trends from specific models would strengthen the rejection of large-scale alternatives.

    Authors: The adopted z ∈ [0.03,0.06] interval was deliberately restricted by our internal consistency diagnostics to minimize selection biases. While a broader baseline could be explored, it would risk introducing new systematics. We will therefore strengthen the analysis by adding an explicit comparison of the observed radial dipole trends against predictions from representative differential-expansion models, thereby providing a more direct test of large-scale alternatives without compromising sample quality. revision: partial

Circularity Check

0 steps flagged

No significant circularity in observational derivation chain

full rationale

The paper conducts an empirical analysis of the Cosmicflows-4 catalogue by comparing angular anisotropy signals in uncorrected versus peculiar-velocity-corrected distance-modulus data, after applying internal consistency diagnostics (depth dependence of mean log H0, residual skewness/kurtosis) to select conservative subsamples such as μ ∈ [31,36] and z ∈ [0.03,0.06]. Spherical-harmonic fits up to octupole order and Bayesian model comparison are performed directly on these data subsets. The central claim—that the dipole is driven by local flows and survey structure rather than large-scale isotropy violation—follows from the observed amplitude reduction after corrections, which is an external empirical outcome not equivalent to any input by construction. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the result to prior author work appear in the derivation; the analysis remains self-contained against the external catalogue and standard corrections.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis relies on standard cosmological assumptions about distance measurements and velocity corrections, plus data-driven choices for conservative subsamples.

free parameters (1)
  • Subsample selection ranges (μ ∈ [31,36] and z ∈ [0.03,0.06])
    Chosen post-hoc from internal consistency tests on depth dependence and residual statistics to minimize selection effects.
axioms (2)
  • domain assumption Logarithmic formulation based on distance moduli preserves Gaussian error properties
    Invoked for the statistical formulation of the Hubble-Lemaître relation.
  • domain assumption Peculiar velocity corrections reliably isolate cosmological expansion signal
    Central to comparing uncorrected and corrected data anisotropy amplitudes.

pith-pipeline@v0.9.0 · 5651 in / 1478 out tokens · 50586 ms · 2026-05-17T02:45:30.409532+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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    Local structure modeled via Λ-Szekeres patches fitted to Cosmicflows-4 data produces a ~0.5 km/s/Mpc upward shift in H0 from Pantheon+ supernovae, increasing the Hubble tension.

Reference graph

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