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arxiv: 2606.07854 · v1 · pith:VFVTIJIAnew · submitted 2026-06-05 · 🌌 astro-ph.CO · gr-qc

Measurements of the Angular Homogeneity Scale from DESI DR1

Mariana Lopes-Dias , Carlos A.P. Bengaly , Xiaoyun Shao , Rodrigo Gon\c{c}alves , Paula S. Ferreira , Gabriela Coutinho de Carvalho , Jailson Alcaniz This is my paper

Pith reviewed 2026-06-27 20:43 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords angular homogeneity scalecosmological principleDESI DR1large-scale structureΛCDM modelgalaxy clusteringstatistical isotropyredshift surveys
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The pith

DESI DR1 data identifies the angular homogeneity scale in every redshift bin from 0.4 to 1.1 and finds values matching ΛCDM mocks.

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

The paper measures the angular homogeneity scale θ_H using two-dimensional projections of luminous red galaxies from DESI DR1, restricted to narrow redshift slices inside 0.4 < z < 1.1. It establishes that this scale is detected in all bins examined, that the measured values match those in mock catalogs built on the standard cosmological model, and that the north and south galactic cap results agree with each other and with earlier eBOSS DR16 measurements. A sympathetic reader cares because these findings test whether the universe meets the statistical homogeneity and isotropy required to apply the FLRW metric for distances and ages. The analysis deliberately stays two-dimensional to limit prior dependence on any specific cosmological model.

Core claim

The angular homogeneity scale is identified in all redshift ranges, and the measured values are consistent with mock simulations assuming the ΛCDM model. The results also show strong agreement with previous measurements from SDSS-IV eBOSS DR16 as well as between the north and south galactic caps of the DESI DR1 survey. These outcomes support statistical homogeneity and isotropy of the universe on large scales.

What carries the argument

The angular homogeneity scale θ_H, extracted from two-dimensional angular galaxy correlations computed inside narrow redshift slices.

If this is right

  • The Cosmological Principle remains a valid working hypothesis for the redshift range and sky regions probed.
  • ΛCDM mock catalogs correctly predict the scale at which angular homogeneity appears.
  • No tension appears between independent surveys or between opposite galactic caps.
  • The same testing approach can be applied directly to forthcoming stage-IV redshift surveys.

Where Pith is reading between the lines

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

  • If three-dimensional analyses recover the same scale, the case for homogeneity would rest on fewer assumptions about projection effects.
  • Persistent agreement across multiple independent surveys suggests that remaining systematic uncertainties in homogeneity measurements are smaller than the statistical errors reported here.
  • Any future claim of large-scale inhomogeneity would need to appear on scales larger than those already tested or in redshift ranges outside 0.4 < z < 1.1.

Load-bearing premise

Performing the analysis exclusively in two dimensions inside narrow redshift slices inside 0.4 < z < 1.1 removes enough dependence on the underlying cosmological model that consistency with mocks can be claimed without circularity.

What would settle it

A measurement in any single redshift bin where the recovered homogeneity scale lies outside the uncertainty range of both the ΛCDM mocks and the earlier eBOSS DR16 values would falsify the reported consistency.

Figures

Figures reproduced from arXiv: 2606.07854 by Carlos A.P. Bengaly, Gabriela Coutinho de Carvalho, Jailson Alcaniz, Mariana Lopes-Dias, Paula S. Ferreira, Rodrigo Gon\c{c}alves, Xiaoyun Shao.

Figure 1
Figure 1. Figure 1: FIG. 1. Histogram of the redshift distribution of LRG’s in the North Galactic Cap (left panel) and South Galactic Cap (right [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Footprint of Galactic Cap. Upper panels show North Hemisphere and bottom panels show South Hemisphere. Left [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Curves of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Measurements of the angular homogeneity scale, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Measurements of the angular homogeneity scale, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Footprint of North Galactic Cap distribution for each redshift range. Upper panel shows the eBOSS DR16 data and [PITH_FULL_IMAGE:figures/full_fig_p018_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Footprint of South Galactic Cap distribution for each redshift range. Upper panel shows the eBOSS DR16 data and [PITH_FULL_IMAGE:figures/full_fig_p018_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Footprint of DESI DR1 catalog distribution for each redshift range. Upper panel shows the North Galactic Cap data [PITH_FULL_IMAGE:figures/full_fig_p019_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Measurements of the correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p020_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Comparison of correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p021_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Comparison of correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p022_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Comparison of correlation matrices for correlation dimension, [PITH_FULL_IMAGE:figures/full_fig_p022_24.png] view at source ↗
read the original abstract

The study of the large-scale distribution of galaxies provides essential information for testing the standard cosmological model, namely the $\Lambda$CDM paradigm. This scenario is based upon two foundations: General Relativity as the theory of gravity, and the Cosmological Principle, which states that the Universe is statistically homogeneous and isotropic on large scales -- so that we can measure distances and ages in the Universe assuming the FLRW metric. In this work, we perform a test of the Cosmological Principle by probing the angular homogeneity scale, $\theta_H$, using the state-of-the-art observational data of Luminous Red Galaxies (LRGs) from the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1). Our analysis is performed exclusively in two dimensions, across narrow redshift ranges inside a larger redshift sample of $0.4 < z < 1.1$, in two different surveyed regions of the sky (North and South Galactic Caps), as we want to minimize a priori dependences on an underlying cosmological model. We obtain that such a scale is indeed identified in all redshift ranges, and that they are consistent with mock simulations assuming the $\Lambda$CDM model. Moreover, our results are in great agreement with previous measurements using Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 (SDSS-IV eBOSS DR16), as well as between the north and south galactic caps of the DESI DR1 survey. These findings help underpinning statistical isotropy and homogeneity of the Universe as a physically valid hypothesis in light of upcoming stage-IV redshift surveys, hence are consistent with one of the fundamental pillars of the standard cosmological model.

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 / 1 minor

Summary. The manuscript reports measurements of the angular homogeneity scale θ_H from DESI DR1 LRG data in narrow redshift slices (0.4 < z < 1.1) using two-dimensional angular statistics in the North and South Galactic Caps. It claims that θ_H is detected in all redshift ranges, is consistent with ΛCDM mock simulations, agrees with previous eBOSS DR16 measurements, and is consistent between the two caps, thereby supporting the Cosmological Principle with minimal cosmological model dependence.

Significance. If the central results hold, the work provides a valuable consistency test of large-scale homogeneity using new, high-quality data from DESI. The agreement between NGC and SGC and with prior surveys is a strength. The approach aims to reduce model dependence through the choice of 2D narrow-slice analysis, which is a positive methodological choice. However, the overall significance for testing the Cosmological Principle is moderated because the validation is performed against mocks that assume the ΛCDM model rather than through a fully model-independent metric.

major comments (2)
  1. [Abstract] The abstract asserts that the homogeneity scale is identified and consistent with mocks but does not provide any quantitative values, error bars, sample sizes, or the precise definition and extraction method for θ_H. This omission makes it impossible to assess whether the data actually support the stated claim of detection and consistency.
  2. [Methods section (narrow redshift slices)] The central claim of achieving minimal a priori dependence on an underlying cosmological model through the use of narrow redshift slices and purely angular 2D measurements is load-bearing for the paper's interpretation. However, the definition of θ_H (via angular correlation function or counts-in-cells) and the random catalog construction still require the survey selection function n(z) and mask, which may embed fiducial cosmology assumptions even in narrow slices. This needs explicit quantification or demonstration that residual dependence is negligible.
minor comments (1)
  1. [Abstract] The phrasing 'in great agreement' is vague; specific quantitative comparison metrics should be provided in the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and constructive suggestions. We have carefully considered the major comments and will make revisions to address them as outlined below.

read point-by-point responses

  1. Referee: [Abstract] The abstract asserts that the homogeneity scale is identified and consistent with mocks but does not provide any quantitative values, error bars, sample sizes, or the precise definition and extraction method for θ_H. This omission makes it impossible to assess whether the data actually support the stated claim of detection and consistency.

    Authors: We agree with this assessment. The revised abstract will include quantitative measurements of θ_H (with 1σ uncertainties) for the redshift bins, the number of galaxies in the NGC and SGC samples, and a concise description of how θ_H is defined and extracted from the angular two-point correlation function in narrow redshift slices. revision: yes

  2. Referee: [Methods section (narrow redshift slices)] The central claim of achieving minimal a priori dependence on an underlying cosmological model through the use of narrow redshift slices and purely angular 2D measurements is load-bearing for the paper's interpretation. However, the definition of θ_H (via angular correlation function or counts-in-cells) and the random catalog construction still require the survey selection function n(z) and mask, which may embed fiducial cosmology assumptions even in narrow slices. This needs explicit quantification or demonstration that residual dependence is negligible.

    Authors: This is a valid concern. Although the narrow slices reduce the dependence significantly by focusing on angular statistics, the random catalogs do use the measured n(z) and the survey mask. In the revised manuscript, we will add a dedicated subsection demonstrating the robustness: we will generate random catalogs with perturbed fiducial cosmologies (varying Ω_m by ±10%) and show that the shifts in θ_H are smaller than the measurement uncertainties, thereby quantifying that the residual dependence is negligible. revision: yes

Circularity Check

0 steps flagged

No circularity: direct data-to-mock comparison with external benchmarks

full rationale

The paper measures θ_H via angular two-point statistics in narrow redshift slices chosen explicitly to reduce model dependence, then compares the resulting scale values directly to independent ΛCDM mock catalogs and to prior eBOSS measurements. No equation or definition in the provided text reduces a claimed result to a fitted parameter or self-citation by construction; the consistency statements rest on external catalogs whose generation is outside the present analysis pipeline.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, invented entities, or additional axioms beyond the standard assumption that mock catalogs faithfully represent Lambda-CDM expectations.

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discussion (0)

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Reference graph

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