⚛️ general relativity

Redshift Dependence of $H_0$ Dipole in Pantheon+ Supernovae

Using the Pantheon+ Type Ia supernovae compilation, this study identifies a statistically significant ( $2-3\sigma$ ) dipole in the local Hubble constant ( $H_0$ ) at low redshifts ( $z \lesssim 0.032$ ) aligned with the Shapley supercluster and CMB dipole, suggesting that observed $H_0$ anisotropy is primarily a low-redshift feature that diminishes as redshift increases.

Original authors: M. H. Jalali-Kanafi, E. Ó Colgáin, S. Pourojaghi, M. M. Sheikh-Jabbari

Published 2026-08-10

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CC BY 4.0

Original authors: M. H. Jalali-Kanafi, E. Ó Colgáin, S. Pourojaghi, M. M. Sheikh-Jabbari

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, expanding balloon. For decades, scientists have believed that if you zoom out far enough, this balloon inflates perfectly evenly in every direction. This idea, called the "Cosmological Principle," suggests that no matter where you stand in the cosmos, the rate at which space stretches—the Hubble constant ( $H_0$ )—should be the same. It's the cosmic rulebook that says the universe is a smooth, fair place. But what if the balloon isn't perfectly smooth? What if, just like a slightly lumpy potato, it stretches a bit faster in one direction and slower in another? This is the big question astronomers are asking: Is the universe truly uniform, or is there a hidden "tilt" in the expansion that we haven't noticed yet?

To investigate this, a team of researchers turned their attention to Type Ia supernovae. Think of these as the universe's "standard candles"—exploding stars that all burn with the same intrinsic brightness. Because we know how bright they should be, we can tell how far away they are by how dim they look. By measuring how fast these stars are moving away from us, scientists can calculate the expansion rate of the universe in different directions. The paper in question, titled "Redshift Dependence of H0 Dipole in Pantheon+ Supernovae," dives deep into a massive collection of these supernovae called Pantheon+ to see if the expansion rate really does have a directional bias, or "dipole," and whether that bias changes as we look at stars that are closer or farther away.

The researchers decided to play a game of "cosmic hide-and-seek" with the data. Instead of looking at the whole universe at once, they sliced the data into different layers based on distance, or "redshift." They started by looking at the very closest supernovae (those with a redshift between 0.015 and 0.2) and then slowly pushed their view further out, ignoring the closest ones to see if the pattern held up. They mapped the expansion rate across the entire sky, dividing it into 48 patches, like a low-resolution globe, to see if one side of the sky was expanding faster than the other.

What they found was a fascinating, albeit temporary, wobble. When they looked at the closest supernovae (starting from a redshift of 0.015), they detected a clear signal: the universe seemed to be expanding faster in one direction than the other. The strength of this "dipole" was measured at $1.16 \pm 0.28$ km/s/Mpc. This isn't just a tiny blip; statistically, it's a significant finding, sitting between 2 and 3 standard deviations ( $\sigma$ ) away from what we'd expect if the universe were perfectly smooth. Interestingly, the direction of this faster expansion points roughly toward a massive cluster of galaxies called the Shapley Supercluster and aligns with the direction of the Cosmic Microwave Background (CMB) dipole—the "wind" we feel as the Earth moves through the universe.

However, the story changes as they look deeper. As the researchers increased the minimum distance of the supernovae they included (moving the starting line from 0.015 up to 0.045), the signal began to fade. By the time they looked at the more distant supernovae, the dipole amplitude dropped to $0.35 \pm 0.52$ km/s/Mpc, a value that is effectively zero and indistinguishable from random noise. The statistical significance of the signal also plummeted, dropping from a confident 3-sigma detection to less than 1-sigma.

This fading act is the paper's most crucial insight. It suggests that the "tilt" in the universe's expansion isn't a fundamental property of the cosmos itself, but rather a local effect. The authors argue that the signal is likely caused by the gravitational pull of nearby massive structures, like the Shapley Supercluster, which are tugging on the local flow of galaxies. As you look further away, beyond the reach of these local gravitational tides, the universe smooths out and returns to the expected uniform expansion. The paper explicitly rules out the idea that this dipole is a sign of a broken cosmological model at large scales; instead, it confirms that the "lumpiness" is a feature of our local neighborhood.

To be absolutely sure this wasn't just a fluke of their math, the team ran 1,000 computer simulations of a perfectly smooth universe (based on the standard $\Lambda$ CDM model) and ran their same analysis on those fake datasets. In almost all those simulations, they didn't see such a strong signal in the closest layers. This comparison gave them confidence that the signal they saw in the real data was real, at least for the nearby universe. They also checked their math carefully, ensuring they accounted for how errors in one part of the sky might affect another, a step that previous studies sometimes missed.

In the end, the paper paints a picture of a universe that is mostly smooth and fair, but has a few local "traffic jams" and "wind tunnels" caused by giant clusters of galaxies. The expansion rate isn't broken; it's just that our local neighborhood is a bit busy. The authors conclude that the Hubble constant, which we try to measure with extreme precision, might actually vary by about 10% across the sky if you only look at the very nearby universe. This means that if we want to measure the universe's expansion rate to within 1% accuracy, we have to be very careful to look far enough away to escape the gravitational influence of our local cosmic neighborhood. The mystery of the "tilt" isn't a crack in the foundation of cosmology, but a reminder that even in a vast, expanding universe, the neighborhood still matters.

Technical Summary: Redshift Dependence of H0 Dipole in Pantheon+ Supernovae

Problem Statement
The Cosmological Principle (CP) posits that the universe is homogeneous and isotropic on large scales, implying the Hubble parameter $H(z)$ depends only on redshift, not direction. However, recent literature suggests potential anisotropies in the local expansion rate ( $H_0$ ), often manifested as a dipole component. While previous studies using Type Ia supernovae (SNe) have reported dipole signals, results vary regarding statistical significance and direction. A key open question is whether these anisotropies are cosmological in origin or local features driven by nearby large-scale structures and bulk flows. Furthermore, the dependence of these signals on the redshift range of the data remains to be systematically quantified.

Methodology
The authors analyze the Pantheon+ compilation of 1,701 spectroscopically confirmed Type Ia SNe, focusing on the low-redshift regime ( $z < 0.2$ ). The study employs a tomographic approach to reconstruct directional maps of $H_0$ across the sky.

Redshift Tomography: The analysis is performed across 10 distinct redshift bins defined by a minimum redshift threshold, $z_{min} \in [0.015, 0.045]$ , with a fixed upper bound of $z_{max} = 0.2$ . This allows the authors to probe how the anisotropic signal evolves as the influence of very local, highly nonlinear environments is progressively removed.
Directional Reconstruction: The sky is discretized using the HEALPix tessellation scheme ( $N_{side}=2$ , resulting in 48 pixels). For each pixel, a spherical cap of $75^\circ$ radius is defined. Within each cap, cosmological parameters ( $H_0$ , $\Omega_m$ , and absolute magnitude $M$ ) are inferred independently using a Bayesian framework within a spatially flat $\Lambda$ CDM model. The analysis utilizes the full Pantheon+ covariance matrix, truncated to the specific SNe within each cap, to properly propagate statistical and systematic uncertainties.
Dipole Decomposition: The reconstructed $H_0$ maps are fitted to a dipole ansatz: $H_0(\hat{n}) = H_0^{mono} + \vec{D} \cdot \hat{n}$ . The dipole amplitude ( $A_{dip}$ ) and direction are extracted using a generalized least-squares (GLS) fit.
Statistical Validation: To assess significance, the authors generate 1,000 Monte Carlo simulations (MC-lcdm) based on an isotropic $\Lambda$ CDM model that preserves the observational characteristics (sky position, redshift distribution, and full covariance structure) of the Pantheon+ data. These simulations serve as a null hypothesis to determine the expected distribution of dipole amplitudes in an isotropic universe.

Key Contributions

Tomographic Analysis: Unlike previous studies that often use fixed redshift ranges or hemisphere decompositions, this work systematically varies $z_{min}$ to isolate the redshift dependence of the $H_0$ dipole.
Rigorous Error Propagation: The study explicitly constructs a full $48 \times 48$ covariance matrix for the sky patches using Monte Carlo realizations. This accounts for correlations between overlapping caps and ensures that errors in $H_0$ are not underestimated, a critical step often overlooked in directional analyses.
Multi-estimator Approach: The authors evaluate anisotropy using three distinct estimators: the dipole amplitude ( $A_{dip}$ ), a conservative significance estimator ( $S$ ), and the maximal antipodal contrast ( $\Delta H_0^{max}$ ).

Results

Redshift Dependence: The dipole amplitude decreases monotonically as $z_{min}$ $z_{min}$ increases.
- At the lowest threshold ( $z_{min} = 0.015$ ), the dipole amplitude is $A_{dip} = 1.16 \pm 0.28$ km/s/Mpc.
- At the highest threshold ( $z_{min} = 0.045$ ), the amplitude drops to $A_{dip} = 0.35 \pm 0.52$ km/s/Mpc, consistent with zero.
Statistical Significance: The significance of the dipole signal is highly dependent on the redshift cut.
- For $z_{min} \lesssim 0.032$ , the dipole signal is statistically significant, ranging between $2\sigma$ and $3.1\sigma$ (depending on the estimator used).
- For $z_{min} \geq 0.038$ , the signal becomes consistent with isotropy (noise).
Direction: For significant bins ( $z_{min} < 0.03$ ), the inferred dipole direction clusters within $\sim 30^\circ$ of the Shapley Supercluster and the CMB dipole direction. As $z_{min}$ increases and the signal vanishes, the direction becomes unstable and drifts.
Higher Multipoles: The authors compare the dipole amplitude to the maximal antipodal contrast ( $\Delta H_0^{max}$ ). They find that $\Delta H_0^{max}/2$ is statistically consistent with the fitted dipole amplitude ( $A_{dip}$ ) for all redshift cuts, suggesting that the anisotropy is dominated by the dipole term rather than higher-order multipoles in the reconstructed maps. However, $\Delta H_0^{max}$ retains a non-zero signal even when $A_{dip}$ is consistent with zero at higher $z_{min}$ , hinting that residual anisotropy may exist but is not captured by the dipole ansatz.

Significance and Claims
The paper claims that the observed $H_0$ dipole is a low-redshift feature rather than a global cosmological effect. The rapid decline in statistical significance as $z_{min}$ increases suggests that the anisotropy is driven by local large-scale structures (potentially the Shapley Supercluster) and coherent peculiar velocity fields (bulk flows) rather than a violation of the Cosmological Principle at cosmological scales.

The authors note that while the dipole signal aligns with the Shapley/CMB directions at low redshifts, the data becomes insufficient to map the Shapley effect using a dipole ansatz beyond $z \approx 0.038$ . They conclude that the Hubble-Lemaître Law may require revision in the local universe to account for these bulk flows, which could impact the precision of $H_0$ determination. The findings support the convergence of literature suggesting that local bulk flows can preclude an isotropic $H_0$ measurement at distances up to $\sim 300 h^{-1}$ Mpc.

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