arxiv: 2605.03004 · v1 · submitted 2026-05-04 · 🌌 astro-ph.CO · gr-qc

Recognition: 3 theorem links

· Lean Theorem

Comparing Hemispheres: Anisotropy in the deceleration parameter q₀

Josue De-Santiago, Mauricio Lopez-Hernandez

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:50 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc

keywords Type Ia supernovaedeceleration parameteranisotropyPantheon+ samplepeculiar velocitiesCMB dipolecosmic accelerationbulk flow

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The pith

Even after full kinematic corrections, a dipolar anisotropy in the deceleration parameter q0 of amplitude 0.112 remains in the Pantheon+ supernovae sample.

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

The paper splits the Pantheon+ Type Ia supernova sample into opposite hemispheres to test whether the deceleration parameter q0 is the same in all directions. It compares results across three redshift frames and finds that a directional variation aligned with the CMB dipole survives even in the z_HD frame after corrections for the solar motion and peculiar velocities have been applied. The amplitude of this variation is Δq0 = 0.112 with a peak signal-to-noise of 2.155, and the signal weakens when the minimum redshift is raised. Replacing the standard velocity corrections with a dipole velocity inferred directly from the supernovae themselves reduces the hemispheric difference to a level consistent with noise. The authors interpret the remaining signal as evidence that current peculiar-velocity models leave a residual bulk flow uncorrected.

Core claim

In the z_HD frame a residual dipolar anisotropy in q0 persists with Δq0 = 0.112 and maximum S/N = 2.155, aligned with the CMB dipole and decreasing with rising minimum redshift cut. Inferring the dipole from the supernovae data themselves yields v⊙ = 307.26 km s^{-1} toward (RA, DEC) = (156.40°, −3.38°), mildly discrepant with the Planck direction at ~1.9σ; substituting this inferred dipole into the correction pipeline suppresses the dipolar pattern and reduces the maximum S/N to ≲ 1.75, leaving only fluctuations consistent with statistical noise.

What carries the argument

Hemispherical comparison of fitted q0 values in three redshift frames (z_hel, z_CMB, z_HD) together with direct dipole inference from the supernova data to isolate and test the effect of residual bulk flow.

If this is right

The anisotropy is stronger in the z_hel and z_CMB frames where kinematic corrections are incomplete.
Incorporating the supernova-inferred dipole into the redshift pipeline removes the dipolar pattern and leaves only noise-level fluctuations.
The signal amplitude decreases as the minimum redshift cut is increased.
Current redshift corrections leave a source of systematic uncertainty in low-redshift supernova cosmology.

Where Pith is reading between the lines

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

If the residual bulk flow is real, it could contribute to apparent variations in the local Hubble constant measured from nearby supernovae.
Future wide-field surveys with improved peculiar-velocity maps could test whether the discrepancy disappears.
The alignment with the CMB dipole direction suggests the effect traces the same large-scale structure that produces the CMB dipole.

Load-bearing premise

Standard peculiar velocity reconstructions based on the density field fully capture the local velocity field, so that any remaining hemispheric difference must be attributed to uncaptured bulk flow.

What would settle it

Detection of the same residual dipolar pattern at comparable significance in an independent low-redshift supernova sample that uses a different velocity-field reconstruction, or a direct measurement showing that local bulk flows exceed the amplitude predicted by current density-field models.

read the original abstract

We present a hemispherical comparison analysis of the deceleration parameter $q_0$ using the Pantheon+ sample of Type Ia supernovae to test the isotropy of cosmic acceleration and the robustness of redshift corrections. We detect directional variations in $q_0$ across redshift frames. Even in the $z_{\mathrm{HD}}$ frame, where corrections for the CMB dipole and peculiar velocities are applied, a residual dipolar anisotropy persists with $\Delta q_0 = 0.112$ and a maximum signal to noise $S/N = 2.155$, aligned with the CMB dipole direction and decreasing with increasing minimum redshift cut. The anisotropy is stronger in the $z_{\mathrm{hel}}$ and $z_{\mathrm{CMB}}$ frames, where kinematic corrections are incomplete, while the transition to $z_{\mathrm{HD}}$ reduces but does not remove the signal. Inferring the dipole from the supernovae data yields $v_{\odot} = 307.26^{+32.00}_{-22.28},\mathrm{km \, s^{-1}}$ toward $(\mathrm{RA},\mathrm{DEC}) = (156.40^{+4.72}_{-4.71}, -3.38^{+5.54}_{-8.23})^\circ$, mildly discrepant with the Planck CMB dipole at the $\sim 1.9\sigma$ level. When this SNe inferred dipole is incorporated into the redshift correction pipeline, the hemispherical anisotropy is suppressed, with the dipolar pattern disappearing and the maximum signal reduced to $S/N \lesssim 1.75$, while the remaining fluctuations become consistent with statistical noise, suggesting that part of the signal arises from residual mismatches in the modeling of the local velocity field. Since current redshift corrections rely on peculiar velocity reconstructions based on the density field, our results suggest a residual bulk flow not fully captured by these models, highlighting a source of systematic uncertainty in low redshift supernova cosmology.

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.

Desk Editor's Note private letter to a colleague

Pantheon+ shows a marginal residual q0 anisotropy after z_HD corrections that drops when an SNe-fitted dipole is substituted, but the numbers are too weak to pin it on missing bulk flow.

read the letter

The paper finds that even in the z_HD frame, where CMB dipole and peculiar-velocity corrections are applied, Pantheon+ still gives a hemispheric difference in q0 of 0.112 with a peak S/N of 2.155, roughly aligned with the CMB dipole. The signal weakens as the minimum redshift cut rises. When the authors fit a dipole velocity directly from the supernovae (307 km/s toward a direction 1.9 sigma off Planck) and re-correct the redshifts, the hemispheric split falls below S/N 1.75 and looks like noise. That is the concrete result they add to the existing literature on supernova isotropy tests.

Referee Report

3 major / 2 minor

Summary. The manuscript performs a hemispherical comparison of the deceleration parameter q0 on the Pantheon+ Type Ia supernova sample across three redshift frames (z_hel, z_CMB, z_HD). It reports a residual dipolar anisotropy persisting in the z_HD frame (after CMB dipole and density-field peculiar-velocity corrections) with Δq0 = 0.112, maximum S/N = 2.155, aligned with the CMB dipole direction and weakening at higher z_min cuts. Fitting a dipole velocity directly from the supernovae (v_⊙ = 307.26^{+32.00}_{-22.28} km s^{-1} toward (RA, DEC) = (156.40^{+4.72}_{-4.71}, -3.38^{+5.54}_{-8.23})°) and re-applying the correction suppresses the pattern to S/N ≲ 1.75, which the authors interpret as evidence for residual bulk flow not captured by current density-field reconstructions.

Significance. If the residual anisotropy is shown to arise specifically from incomplete bulk-flow modeling rather than unaccounted systematics, the result would flag a non-negligible systematic uncertainty for low-redshift supernova cosmology and motivate improved velocity-field reconstructions. The quantitative hemispheric differences, the z_min dependence, and the explicit demonstration that an SNe-derived dipole removes the signal are concrete and potentially useful; however, the marginal S/N and the circularity of the fitting procedure limit the immediate impact on the field.

major comments (3)

[Abstract and §4] Abstract and §4 (results): The quoted values Δq0 = 0.112 and S/N = 2.155 are presented without accompanying covariance matrices, full error budgets, or explicit tests for survey selection, calibration, or light-curve-fitting systematics that could produce sky-correlated residuals. This omission makes it impossible to determine whether the reported 2.155 S/N exceeds plausible unmodeled biases.
[Abstract and §5] Abstract and §5 (discussion): The procedure of inferring the dipole amplitude and direction from the same Pantheon+ data and then re-correcting the redshifts to suppress the anisotropy (S/N dropping to ≲ 1.75) is internally consistent but circular for testing residual bulk flow. Any directional calibration or selection effect present in the sample can be absorbed into the fitted dipole, so the suppression does not uniquely demonstrate an incomplete density-field velocity model.
[Abstract] Abstract: The reported ~1.9σ directional offset between the SNe-inferred dipole and the Planck CMB dipole is cited, yet no quantitative test is provided that isolates this offset from other possible directional systematics (e.g., hemispheric differences in host-galaxy properties or survey depth). Without such a test the attribution to residual bulk flow remains one of several viable interpretations.

minor comments (2)

Notation for the three redshift frames (z_hel, z_CMB, z_HD) should be defined at first use with explicit formulas for the corrections applied in each case.
The abstract states that the anisotropy 'decreases with increasing minimum redshift cut' but does not report the quantitative trend or the z_min values at which S/N falls below a chosen threshold; a table or figure panel would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment point by point below and indicate where we will revise the manuscript to strengthen the presentation.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (results): The quoted values Δq0 = 0.112 and S/N = 2.155 are presented without accompanying covariance matrices, full error budgets, or explicit tests for survey selection, calibration, or light-curve-fitting systematics that could produce sky-correlated residuals. This omission makes it impossible to determine whether the reported 2.155 S/N exceeds plausible unmodeled biases.

Authors: We agree that including the covariance matrices and a fuller error budget would improve transparency. In the revised manuscript we will add the covariance matrices for the hemispheric q0 fits in §4, expand the error budget discussion to cover survey selection, calibration, and light-curve-fitting systematics, and report additional tests quantifying their possible contribution to sky-correlated residuals. revision: yes
Referee: [Abstract and §5] Abstract and §5 (discussion): The procedure of inferring the dipole amplitude and direction from the same Pantheon+ data and then re-correcting the redshifts to suppress the anisotropy (S/N dropping to ≲ 1.75) is internally consistent but circular for testing residual bulk flow. Any directional calibration or selection effect present in the sample can be absorbed into the fitted dipole, so the suppression does not uniquely demonstrate an incomplete density-field velocity model.

Authors: We acknowledge the circularity inherent in fitting the dipole from the same sample. The suppression to S/N ≲ 1.75 demonstrates that a dipole model can account for the observed anisotropy, and the fitted direction remains consistent with the CMB dipole. In the revised §5 we will explicitly note this limitation, clarify that the result is indicative rather than a unique proof of incomplete density-field modeling, and discuss how future independent velocity-field reconstructions could break the degeneracy. revision: partial
Referee: [Abstract] Abstract: The reported ~1.9σ directional offset between the SNe-inferred dipole and the Planck CMB dipole is cited, yet no quantitative test is provided that isolates this offset from other possible directional systematics (e.g., hemispheric differences in host-galaxy properties or survey depth). Without such a test the attribution to residual bulk flow remains one of several viable interpretations.

Authors: We agree that isolating the directional offset from other systematics would strengthen the interpretation. In the revised manuscript we will add quantitative tests in §4 and §5 for hemispheric differences in host-galaxy properties and survey depth, and discuss their possible influence on the reported ~1.9σ offset. revision: yes

Circularity Check

1 steps flagged

Fitting dipole from same SNe data then showing anisotropy suppression is tautological

specific steps

fitted input called prediction [Abstract (dipole inference paragraph)]
"Inferring the dipole from the supernovae data yields v_⊙ = 307.26^{+32.00}_{-22.28} km s^{-1} toward (RA,DEC) = (156.40^{+4.72}_{-4.71}, -3.38^{+5.54}_{-8.23})^∘, mildly discrepant with the Planck CMB dipole at the ∼1.9σ level. When this SNe inferred dipole is incorporated into the redshift correction pipeline, the hemispherical anisotropy is suppressed, with the dipolar pattern disappearing and the maximum signal reduced to S/N ≲ 1.75, while the remaining fluctuations become consistent with statistical noise, suggesting that part of the signal arises from residual mismatches in the modeling"

The dipole parameters are fitted to the same supernova sample whose q0 hemispheric differences are being tested. Re-correcting the redshifts with this fit and observing the signal suppression is guaranteed by construction: any directional pattern in the data is absorbed into the fitted v_⊙ and direction, so the 'disappearance' does not independently confirm a bulk-flow origin versus unmodeled systematics.

full rationale

The paper detects residual q0 anisotropy in z_HD frame (independent measurement across frames). However, it then fits a dipole amplitude/direction directly to the identical Pantheon+ SNe dataset and re-applies that fit as a redshift correction, after which the anisotropy vanishes. This step reduces the 'evidence for residual bulk flow' to a fitted-input-called-prediction that is statistically forced. No other circular patterns (self-citation chains, ansatz smuggling, or renaming) appear in the provided text. The initial frame-to-frame comparison retains independent content, so overall circularity is moderate.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the Pantheon+ catalog being free of directional selection bias after standard cuts, on the accuracy of published peculiar-velocity reconstructions, and on the assumption that any remaining signal after z_HD correction is due to bulk flow rather than other systematics.

free parameters (1)

SNe-inferred dipole velocity
Amplitude and direction fitted directly to the supernova data to test suppression of the anisotropy signal.

axioms (1)

domain assumption Pantheon+ distance moduli remain unbiased after the chosen redshift corrections and quality cuts.
Central to interpreting any residual hemispheric difference as a velocity-field mismatch.

pith-pipeline@v0.9.0 · 5659 in / 1394 out tokens · 56160 ms · 2026-05-08T17:50:58.483376+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith.Cost.FunctionalEquation (J-cost machinery) — not invoked washburn_uniqueness_aczel unclear
we model the observed corrected apparent magnitudes... using a cosmographic expansion of the luminosity distance including terms up to third order in redshift... m_B^th(z) = 5 log10[c z (1 + ½(1−q₀)z − ⅙(1−q₀−3q₀²+j₀)z²)] + M

Reference graph

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