Accelerating expansion and isotropic sky-hemisphere consistency in Pantheon+ supernovae: a revised analysis in the dark energy debate

Technical Summary: Accelerating Expansion and Isotropic Sky-Hemisphere Consistency in Pantheon+ Supernovae

Problem Statement
This paper addresses a recent debate regarding the interpretation of Type Ia supernova (SNe Ia) data from the Pantheon+ catalogue. Specifically, it responds to claims by Sah, Rameez & Sarkar (SRS26) that a proposed progenitor-age correction (Son et al., S25) implies a decelerating universe and a strong dipole anisotropy aligned with the Cosmic Microwave Background (CMB) bulk flow. These claims challenge the standard $\Lambda$CDM model and the evidence for cosmic acceleration. The authors note that their original analysis, which reported a near-zero baseline acceleration and strong deceleration under the S25 correction, contained a critical coordinate error: the CMB dipole direction was treated using Galactic coordinates ($\ell, b$) as if they were equatorial coordinates (RA/Dec). This paper presents a revised analysis correcting this error and re-evaluating the full pipeline.

Methodology
The authors perform four independent decompositions of the deceleration parameter $q_0$ using a subset of 1,564 SNe Ia from the Pantheon+ catalogue (redshift range $0.00937 < z_{hel} \le 0.8$). The analysis utilizes the SALT2 standardization parameters ($m_B, x_1, c$), host galaxy stellar mass, and sky coordinates.

Key methodological steps include:

1. Coordinate Correction: The sky-hemisphere test now correctly projects supernovae onto the CMB dipole direction using ICRS equatorial coordinates (RA = $167.80^\circ$, Dec = $-7.10^\circ$), rather than the erroneous Galactic-to-equatorial conversion used previously.
2. Progenitor-Age Correction: The analysis applies the S25 magnitude correction, $\Delta m(z) = \Delta \text{age}(z) \times 0.030 \text{ mag Gyr}^{-1}$, derived from the supernova delay-time distribution and cosmic star-formation history.
3. Decomposition Tests: The dataset is split and analyzed independently across four categories:
   • Redshift Bins: Five bins ranging from $z \approx 0.01$ to $0.8$.
   • Sky Hemispheres: Split by the corrected CMB dipole (dipole vs. anti-dipole) and North/South celestial hemispheres.
   • Host Galaxy Mass: Split at $\log(M_*/M_\odot) = 10$.
   • Supernova Colour: Split at the median color $c_{med} = -0.031$.
4. Fitting Procedure: Parameters ($H_0, q_0, M, \alpha, \beta$) are estimated by minimizing $\chi^2$ assuming a uniform photometric uncertainty of $\sigma = 0.15$ mag. The luminosity distance is expanded to second order in redshift with $j_0$ fixed at 1.

Key Results
The revised analysis yields results that are inconsistent with the SRS26 claims of a decelerating universe and inconsistent with the authors' original (erroneous) findings of near-zero acceleration.

• Baseline Acceleration: Without any age correction, the full sample yields a deceleration parameter $q_m = -0.490$. This is consistent with the $\Lambda$CDM expectation of $q_0 = -0.55$.
• Effect of S25 Correction: Applying the S25 progenitor-age correction shifts the baseline $q_m$ to $-0.267$. Crucially, the value remains negative, indicating the universe is still in an accelerating regime, contrary to SRS26's claim of a positive (decelerating) $q_m$.
• Redshift Dependence: Across all five redshift bins, the data indicates acceleration both before and after the S25 correction. No sign reversal (from negative to positive $q_m$) is observed in any bin, including the low-redshift bins where SRS26 reported strong deceleration.
• Isotropy (Sky Hemisphere): Using the corrected coordinates, the dipole hemisphere ($N=538$) yields $q_m = -0.527$, and the anti-dipole hemisphere ($N=1026$) yields $q_m = -0.464$. The difference ($\Delta q_m \approx 0.06$) is small, supporting isotropy and ruling out the strong dipole anisotropy claimed by SRS26.
• Host Mass and Colour: Subsamples divided by host mass and supernova colour remain mutually consistent and in the accelerating regime both with and without the S25 correction.

Significance and Claims
The paper concludes that the Pantheon+ data, when analyzed with the corrected coordinates and standard SALT2 standardization, robustly supports the standard $\Lambda$CDM model.

• Refutation of Deceleration Claims: The analysis explicitly rejects the SRS26 claim that the S25 correction implies a decelerating universe. The corrected $q_m$ remains negative ($-0.267$), confirming acceleration.
• Refutation of Anisotropy Claims: The sky-hemisphere test demonstrates that the acceleration signal is isotropic, contradicting the claim that the signal aligns with the CMB bulk flow to suggest a violation of the cosmological principle.
• Consistency with Early Universe Physics: The authors note that while these results revise the late-time expansion history, they do not alter the concordance between Big Bang Nucleosynthesis (BBN) and CMB measurements regarding the primordial baryon density ($\Omega_b h^2$).
• Resolution of Internal Discrepancy: The authors acknowledge that while the coordinate error explains the change in sample sizes for the hemisphere test, it does not fully explain why their original full-sample baseline ($q_m = -0.062$) could not be reproduced even in the absence of the coordinate error. They attribute the bulk of the numerical change to a combination of the coordinate fix and other unidentified differences between their original implementation and the current pipeline reconstruction.

The authors state that their revised results are consistent with standard $\Lambda$CDM and do not support either the original claim of near-zero baseline acceleration or the S25/SRS26 claim of a decelerating, anisotropic universe. They suggest that future data from the Rubin Observatory LSST will provide the statistical power necessary to definitively resolve remaining systematic questions.