⚛️ general relativity

Response to: "Isotropic deceleration and near-zero baseline acceleration in Pantheon+ supernovae: new arguments in the dark energy debate''

This paper refutes Ray et al.'s claim that Pantheon+ supernova data shows isotropic deceleration by demonstrating that their conclusion is baseless due to a fundamental error in confusing Equatorial and Galactic coordinates, which led to an incorrect identification of the CMB dipole direction.

Original authors: Animesh Sah, Mohamed Rameez, Subir Sarkar

Published 2026-08-04

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CC BY 4.0

Original authors: Animesh Sah, Mohamed Rameez, Subir Sarkar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible ocean where galaxies are like buoys floating on the surface. For decades, astronomers have been watching these buoys drift apart, trying to figure out if the ocean is just drifting lazily or if something invisible is pushing them apart faster and faster. This "something" is called dark energy, a mysterious force that scientists believe is making the universe's expansion speed up. To measure this, they look at special exploding stars called Type Ia supernovae, which act like cosmic lighthouses. By checking how bright they look from Earth, scientists can tell how fast the universe is stretching. The big question is: Is the universe speeding up everywhere equally, or is it a bit wobbly, with some parts expanding faster than others? This matters because if the expansion isn't uniform, it could mean our current understanding of the universe's invisible fuel is wrong, or that we are simply looking at the universe from a tilted, moving boat.

Now, enter a new study that acts like a cosmic fact-checker. A team of researchers recently claimed they had solved a puzzle about this expansion. They said they split the sky into two halves—one facing the direction the universe is "moving" (the CMB dipole) and one facing the opposite way—and found that the expansion was speeding up just as much in both halves. They used this to argue against a previous idea that suggested the expansion was actually slowing down in a specific direction (a dipole anisotropy), which would mean the "dark energy" story might be flawed. However, the authors of this new paper, Sah, Rameez, and Sarkar, have spotted a massive mix-up in the other team's math. They argue that the previous researchers confused two different ways of mapping the sky, like using a street map when you needed a subway map.

Here is the core of the mix-up: The universe is huge, so astronomers use coordinate systems to pinpoint where things are, just like latitude and longitude on Earth. One system is "Galactic," which is based on the plane of our own Milky Way galaxy, and the other is "Equatorial," which is based on Earth's rotation and is the standard for most star catalogs. The previous study claimed to use the direction of the "CMB dipole" (the direction the universe is moving) to split their data. They wrote down the coordinates as (264°, 48°) and labeled them as Galactic. But when they did their calculations, they treated those numbers as if they were Equatorial coordinates without converting them first.

The authors of this paper show that this was a critical error. If you take the numbers (264°, 48°) and treat them as Equatorial coordinates, you are pointing your telescope in the completely wrong spot in the sky. It's like trying to find a friend in a city by looking at the address of a building in a different country because you forgot to switch the map. When the authors corrected this mistake and used the proper Equatorial coordinates for the CMB dipole—which are actually (167.8°, −7.1°)—the split of the supernova data changed dramatically. Instead of the roughly even split the other team found (724 supernovae on one side, 840 on the other), the correct split puts 539 supernovae on one side and 1,025 on the other.

Because the original study was looking at the wrong direction in the sky, their conclusion that the expansion is perfectly uniform and contradicts the "tilted observer" idea falls apart. The authors point out that if you actually look in the direction the other team thought they were looking (using the unconverted numbers), there is no evidence of a dipole at all, which makes sense because that direction isn't the real CMB dipole. In short, the paper concludes that the claim of "isotropic deceleration" (uniform slowing down) based on that specific analysis is baseless. The error was purely technical—a coordinate mix-up—but it was enough to invalidate the argument that the universe's expansion is perfectly smooth in the way they claimed. The debate about whether the universe is accelerating uniformly or if there is a directional tilt remains open, but this specific attempt to close the case has been shown to be built on a wrong map.

Technical Summary: Response to "Isotropic deceleration and near-zero baseline acceleration in Pantheon+ supernovae"

Problem Statement
Ray et al. [1] (hereafter R26) recently claimed that the acceleration of the Hubble expansion rate, inferred from Type Ia supernovae (SNe Ia) in the Pantheon+ catalogue, exhibits no significant hemispheric asymmetry. Specifically, they argued that the deceleration parameter $q_0$ is equally strong in the Cosmic Microwave Background (CMB) dipole and anti-dipole hemispheres ( $q_m \approx +1.45$ and $+1.55$ , respectively). This conclusion directly contradicts the findings of Sah et al. [2] (SRS26), which reported a strong dipole anisotropy in the locally inferred $q_0$ aligned with the bulk flow, leaving only a small monopole component at larger distances. The core issue addressed in this response is the validity of R26's hemispheric test, which the authors argue is fundamentally flawed due to a coordinate system error.

Methodology
The authors re-evaluate the sample selection and coordinate transformation procedures used by R26. The Pantheon+SH0ES data release [6] tabulates supernova sky positions in equatorial coordinates (ICRS: Right Ascension $\alpha$ and Declination $\delta$ ). To compute the angle $\theta$ between a supernova and a reference direction, the dot product formula requires consistent coordinate systems:
$\cos \theta = \sin \delta \sin \delta_0 + \cos \delta \cos \delta_0 \cos(\alpha - \alpha_0)$
R26 stated their reference direction as the CMB dipole in Galactic coordinates $(\ell, b) = (264^\circ, 48^\circ)$ . However, the authors demonstrate that R26 applied these numerical values directly as equatorial coordinates $(\alpha_0, \delta_0)$ without performing the necessary transformation from Galactic to ICRS.

To test this hypothesis, the authors reproduce the R26 sample selection ( $N=1564$ SNe Ia in the redshift range $0.00937 < z_{hel} \le 0.8$ ) and evaluate Eq. (1) under two distinct interpretations of the reference direction:

Incorrect Interpretation: Treating the values $(264^\circ, 48^\circ)$ as equatorial coordinates $(\alpha_0, \delta_0)$ , effectively ignoring the Galactic label.
Correct Interpretation: Using the properly transformed CMB dipole direction in equatorial coordinates, $(\alpha_0, \delta_0) = (167.8^\circ, -7.1^\circ)$ .

Key Results
The analysis yields two distinct partitions of the supernova sample:

Reproducing R26's Error: When using the untransformed values $(264^\circ, 48^\circ)$ as equatorial coordinates, the sample splits into $N=724$ (where $\cos \theta \ge 0$ ) and $N=840$ (where $\cos \theta < 0$ ). This matches the numbers reported in the caption of R26's Fig. 3, confirming that R26 erroneously treated Galactic coordinates as equatorial.
Corrected Partition: When using the true CMB dipole direction in equatorial coordinates $(167.8^\circ, -7.1^\circ)$ , the sample splits significantly differently into $N=539$ and $N=1025$ .

Furthermore, when the authors fit a dipole model using the direction $(264^\circ, 48^\circ)$ interpreted as equatorial coordinates, they find a likelihood difference $\Delta LLH \approx 0.2$ , indicating no evidence for a dipole in that specific direction. This is consistent with the fact that $(264^\circ, 48^\circ)$ in equatorial coordinates does not correspond to the CMB dipole.

Significance and Conclusion
The paper concludes that the hemispheric test presented in R26 is not centered on the CMB dipole direction due to a technical error in coordinate transformation. Consequently, the assertion by Ray et al. [1] that their results contradict the anisotropy findings of Sah et al. [2] is baseless. The authors maintain that the significant dipole anisotropy in $q_0$ aligned with the CMB dipole, as reported in SRS26, remains valid and continues to argue against a purely isotropic cosmic acceleration driven by dark energy. The response serves to correct the methodological record regarding the Pantheon+ sample analysis.

Technical Summary: Response to "Isotropic deceleration and near-zero baseline acceleration in Pantheon+ supernovae"

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