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arxiv: 2605.18470 · v1 · pith:HXHUPHMLnew · submitted 2026-05-18 · 🌌 astro-ph.CO

(An)Isotropy in Pantheon+ and Type Ia supernova samples: intrinsic limits of directional tests

Antonio Quintana-Estell\'es , Pilar Ruiz-Lapuente This is my paper

Pith reviewed 2026-05-20 09:17 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Hubble constant anisotropyType Ia supernovaePantheon+ sampleisotropy testsRegion Fitting methodHemisphere Comparisoncosmological isotropy
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The pith

Current supernova samples cannot robustly determine directions of Hubble constant anisotropy.

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

This paper applies Region Fitting and Hemisphere Comparison methods to the Pantheon+ database and a smaller Carnegie Supernova Project sample to test for directional variations in the Hubble constant. Using MCMC sampling over 2000 directions, the analysis shows that apparent anisotropy directions arise from statistical fluctuations tied to uneven sky coverage and the way H0 is extracted from supernova light curves. The same limitation appears in both datasets, explaining contradictory results in earlier studies. A sympathetic reader cares because this bears on whether the universe is isotropic at large scales and whether current data can settle the question.

Core claim

Within the tests used here, the Region Fitting method and the Hemisphere Comparison method, one can not determine with robustness the direction of an anisotropy of H0 using the present SNe Ia large data samples. This is intrinsic to the way H0 is obtained with the SN Ia lightcurve method. Achieving robust constraints will require a quite uniform sky coverage from larger SNe Ia samples with improved systematics.

What carries the argument

Region Fitting and Hemisphere Comparison methods, which compare H0 values across sky patches of 60 or 90 degrees via MCMC sampling over many directions, to probe isotropy while limited by data distribution and lightcurve-derived uncertainties.

If this is right

  • Apparent anisotropy directions vary across samples and methods because of statistical fluctuations from current sky coverage.
  • The intrinsic limit prevents robust directional claims for H0 with existing large SNe Ia databases.
  • Larger samples with improved systematics and uniform coverage are required to place reliable constraints on isotropy.

Where Pith is reading between the lines

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

  • Earlier reports of specific anisotropy directions are likely artifacts of sampling rather than cosmological signals.
  • Tests of the cosmological principle using supernova data must first correct for coverage biases before interpreting any preferred direction.
  • Surveys that aim for even sky distribution will be needed to turn directional H0 measurements into decisive isotropy tests.

Load-bearing premise

The Region Fitting and Hemisphere Comparison methods can separate genuine directional changes in H0 from fluctuations caused by the present uneven sky distribution of supernovae and their measurement errors.

What would settle it

A large future supernova sample with nearly uniform sky coverage that yields the same anisotropy direction in both Region Fitting and Hemisphere Comparison analyses, even after tightening systematics, would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.18470 by Antonio Quintana-Estell\'es, Pilar Ruiz-Lapuente.

Figure 1
Figure 1. Figure 1: SNe Ia distribution in galactic coordinates, with the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Redshift histogram for Pantheon+ dataset. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Individual H0 values derived by inverting the dis￾tance–redshift relation for SNe Ia. Pantheon+ dataset. 50 60 70 80 90 100 110 120 H0 (km/s/Mpc) 0 50 100 150 200 250 300 350 400 Number Pantheon+SH0ES [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Histogram of individual H0, i values. More interestingly, we present in [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: RF method applied to Pantheon+ dataset with [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Probability density contours for Pantheon+ with the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: HC method applied to CSP dataset with all 25 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left: Redshift distribution of the CSP sample. Right: [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: Results of simulations including an intrinsic scatter [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Probability density contours for CSP from the HC [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

The use of methods that investigate the value of the Hubble constant H$_0$ in different patches (60 $ or 90$^ size) across the sky to probe the statistical isotropy of the Universe using large SNe Ia databases has led to contradictory claims of either anisotropy or isotropy. The anisotropy directions vary amongst research works. The objective of this paper is to clarify the abovementioned claims and study the lack of basis for depicting directions of anisotropy with the present SNe Ia samples. We explain the type of limitation embedded in the SN Ia lightcurve method to determine the isotropy of H_0 and the corresponding consequences. The widely used analysis through the Region Fitting and the Hemisphere Comparison methods is done here using the Pantheon+ database, simulating 2000 distinct directions in the sky within a Bayesian Markov Chain Monte Carlo approach. We also study a smaller SNe Ia database, the Carnegie Supernova Project sample, leading to a similar kind of result as that from the Pantheon+ sample. We investigate the validity of the directions found for anisotropy within these analyses. We have found that within the tests used here, the Region Fitting method and the Hemisphere Comparison method, one can not determine with robustness the direction of an anisotropy of H$_0$ using the present SNe Ia large data samples. This is intrinsic to the way H$_0$ is obtained with the SN Ia lightcurve method. Achieving robust constraints will require a quite uniform sky coverage from larger SNe Ia samples with improved systematics.

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

1 major / 2 minor

Summary. The paper analyzes claims of statistical anisotropy in the Hubble constant H0 derived from Type Ia supernovae by applying the Region Fitting and Hemisphere Comparison methods to the Pantheon+ catalog and the smaller Carnegie Supernova Project sample. Using Bayesian MCMC sampling over 2000 distinct sky directions, the authors simulate the effects of current sky coverage and measurement uncertainties and conclude that these standard directional tests cannot robustly recover anisotropy directions; any apparent directions are dominated by statistical fluctuations intrinsic to the SN Ia light-curve fitting procedure. They argue that substantially more uniform sky coverage from future larger samples will be required for reliable isotropy constraints.

Significance. If the central result holds, the work supplies a concrete methodological explanation for the contradictory anisotropy directions reported across the recent literature. The direct comparison of two independent public samples, the explicit MCMC exploration of many directions, and the reproduction of the same limitation in both datasets constitute a falsifiable demonstration that current SN Ia compilations are intrinsically limited for this class of test. This finding should temper interpretations of directional H0 variations and inform the design of next-generation surveys.

major comments (1)
  1. The manuscript demonstrates through simulations that statistical fluctuations from sky distribution and uncertainties dominate the recovered directions, but it would strengthen the central claim to include a quantitative metric (e.g., the fraction of MCMC realizations in which the recovered direction lies within 30° of the input direction) for both the isotropic and mildly anisotropic mock catalogs.
minor comments (2)
  1. Abstract, line 3: the notation '60 $ or 90$^ size' contains a clear typesetting error and should read '60° or 90° patches'.
  2. The description of the MCMC sampling (number of chains, convergence diagnostics, and prior choices on the directional parameters) is only summarized; a short appendix or subsection with these technical details would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for the constructive suggestion. We address the single major comment below.

read point-by-point responses

  1. Referee: The manuscript demonstrates through simulations that statistical fluctuations from sky distribution and uncertainties dominate the recovered directions, but it would strengthen the central claim to include a quantitative metric (e.g., the fraction of MCMC realizations in which the recovered direction lies within 30° of the input direction) for both the isotropic and mildly anisotropic mock catalogs.

    Authors: We agree that a quantitative metric of this type would strengthen the presentation of our results. In the revised manuscript we will add the fraction of MCMC realizations in which the recovered direction lies within 30° of the input direction, computed separately for the isotropic and mildly anisotropic mock catalogs. This will be reported in the sections describing the simulation results. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper applies the standard Region Fitting and Hemisphere Comparison methods via MCMC sampling over 2000 simulated directions to the external Pantheon+ and CSP supernova catalogs. Its central conclusion—that anisotropy directions in H0 cannot be robustly recovered due to intrinsic limits from the SN Ia lightcurve method and current sky coverage—follows directly from these simulations of statistical fluctuations and measurement uncertainties. No equations, fitted parameters, or self-citations are shown to reduce the result by construction to a quantity defined by the paper's own inputs. The analysis remains self-contained against external public data benchmarks without load-bearing reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard cosmological assumptions about Type Ia supernovae as direction-independent distance indicators and on the statistical validity of the two directional comparison methods; no new entities or ad-hoc parameters are introduced.

axioms (1)
  • domain assumption SN Ia light-curve distances can be treated as direction-independent standard candles for isotropy tests.
    This premise underlies the use of the samples to probe H0 anisotropy and is invoked when interpreting the fitting results.

pith-pipeline@v0.9.0 · 5809 in / 1275 out tokens · 42300 ms · 2026-05-20T09:17:23.863552+00:00 · methodology

discussion (0)

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