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No evidence for local $H_0$ anisotropy from Tully--Fisher or supernova distances

Although the study detects statistically significant dipole signals in Tully-Fisher and supernova zero-points, it concludes that these anisotropies are artifacts of local flow features or systematics rather than evidence for a genuine local anisotropy in the Hubble constant, as the results remain fully consistent with the standard cosmological model when accounting for a radially varying bulk flow.

Original authors: Richard Stiskalek, Harry Desmond, Guilhem Lavaux

Published 2026-01-28

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CC BY 4.0

Original authors: Richard Stiskalek, Harry Desmond, Guilhem Lavaux

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

The Big Question: Is the Universe "Fair"?

Imagine the Universe as a giant, perfectly smooth ocean. For decades, scientists have believed in a rule called the Cosmological Principle, which says that if you zoom out far enough, the ocean looks the same no matter which direction you look. It's isotropic (the same in all directions) and homogeneous (evenly spread out).

However, some recent studies suggested the ocean might actually be "sloped." They claimed that the Hubble Constant (the speed at which the universe is expanding) is faster in one direction and slower in another. If true, this would mean the universe isn't fair; it has a "tilt."

This paper asks: Is that tilt real, or is it just an illusion caused by local currents?

The Tools: Measuring the "Speed" of the Universe

To measure how fast the universe is expanding, astronomers use "standard candles"—objects that we know how bright they should be.

Tully-Fisher Galaxies: Think of these as spinning galaxies. The faster they spin, the brighter they are. By measuring how fast they spin and how bright they look, we can calculate their distance.
Supernovae: These are exploding stars that act like very bright lightbulbs. If we know how bright a lightbulb is supposed to be, we can tell how far away it is by how dim it looks.

The authors looked at two massive lists of these objects (galaxies and supernovae) that are relatively close to us (less than 5% of the way across the observable universe).

The Investigation: The "Local Current" Problem

Here is the tricky part: The universe isn't just expanding; galaxies are also moving around due to gravity, like leaves swirling in a stream. This is called peculiar velocity.

Imagine you are trying to measure the speed of a river (the expansion of the universe). But you are standing on a boat that is also drifting with the current (the local flow). If you don't account for your boat's drift, you might think the river is flowing faster or slower than it actually is.

The authors built a sophisticated computer model to:

Map the "drift" (peculiar velocities) of these galaxies.
Subtract that drift to see the true expansion speed.
Check if the expansion speed still looks different in different directions after the drift is removed.

The Findings: A "False Alarm"

When the authors ran their numbers, they found something interesting:

1. The "Tilt" Appears Real (At First Glance)
When they looked at the data without fully accounting for the complex local flows, they found a "dipole"—a direction where things seemed to be expanding faster.

In their galaxy data, this looked like a 4.1% difference in expansion speed between one side of the sky and the other.
In their supernova data, it looked like a 2.3% difference.
Statistically, the data strongly preferred a model that included this tilt over a model that assumed the universe was perfectly flat.

2. The "Tilt" is Actually a Local Current
However, the authors dug deeper. They asked: What if this "tilt" isn't the universe expanding unevenly, but just a massive, local flow of galaxies moving together that our models didn't fully catch?

They tested a more flexible model that allowed the "drift" (the local flow) to change strength as you go further out, rather than assuming it was constant.

The Result: When they allowed the local flow to vary, the "tilt" in the expansion speed disappeared.
The Analogy: It's like thinking the wind is blowing harder in one direction, but realizing you are just standing on a hill where the wind naturally speeds up and then dies down. Once you account for the hill, the wind is actually blowing evenly.

The data showed that the "tilt" was actually a bulk flow (a giant group of galaxies moving together) that rises a bit and then fades away. This behavior is exactly what our standard model of the universe (Lambda-CDM) predicts. It does not show the linear, ever-increasing slope that would prove the universe is fundamentally tilted.

The Conclusion: The Ocean is Still Smooth

The paper concludes that while there are statistical hints of a "tilt" in the data, it is almost certainly not evidence that the universe is anisotropic (different in different directions).

Instead, the "tilt" is likely caused by:

Local currents: Complex movements of galaxies near us that are hard to map perfectly.
Systematic errors: Small imperfections in how we measure light or dust in our own galaxy.

The Takeaway:
The authors found that if you look at the data with a rigid model, you see a "tilt." But if you use a flexible model that accounts for the messy, swirling local currents of our cosmic neighborhood, the tilt vanishes. The universe still looks the same in every direction, and the Cosmological Principle remains safe.

In short: The universe isn't tilted; we just live in a neighborhood with some strong local winds that confused the measurements.

Technical Summary: No evidence for local $H_0$ anisotropy from Tully–Fisher or supernova distances

Problem Statement
Recent claims suggest a local ( $z \lesssim 0.05$ ) anisotropy in the Hubble constant ( $H_0$ ), potentially violating the Cosmological Principle (CP). These claims rely on direct distance tracers, specifically Tully–Fisher relation (TFR) galaxies and Type Ia supernovae (SNe). A critical challenge in testing this hypothesis is the degeneracy between an anisotropy in $H_0$ and an anisotropy in the zero-point calibration of the distance indicators (the TFR zero-point or the standardised SN absolute magnitude). Without an absolute distance calibration, a detected dipole in the combined parameter space could arise from either a true cosmological anisotropy or a systematic error in the distance ladder. Furthermore, local peculiar velocities can mimic such signals if not accurately modeled.

Methodology
The authors employ a forward-modelling framework to jointly calibrate distance relations, marginalise over true distances, and account for peculiar velocities. The analysis utilizes four distinct datasets restricted to $z < 0.05$ :

CosmicFlows-4 (CF4): The W1-band TFR subsample (3246 galaxies).
2MTF: An all-sky TFR sample (1247 galaxies).
SFI++: An all-sky TFR catalogue (2010 galaxies).
Pantheon+: A compilation of Type Ia SNe (525 SNe), including a reanalysis variant (Pantheon+Lane) with a modified covariance matrix.

Key methodological components include:

Peculiar Velocity Modeling: The authors use the linear-theory reconstruction of Carrick et al. (2015, C15) based on the 2M++ galaxy density field to model the internal flow. They introduce an external flow term ( $V_{ext}$ ) and test for a radially varying $V_{ext}(r)$ to distinguish between a constant flow and a linearly growing flow (which would indicate $H_0$ anisotropy).
Forward Modeling: Unlike previous "backward" approaches that infer cosmological redshifts from observed redshifts (introducing complications in triple-valued zones), this work models observed redshifts directly by querying the velocity field in real space.
Dipole Parameterization: The model introduces a dipole term ( $\Delta ZP$ ) to the degenerate combination of the TFR zero-point and $H_0$ (or the SN absolute magnitude and $H_0$ ).
Systematics Control: The study explicitly tests the impact of Galactic extinction by comparing results using Schlegel et al. (1998), Chiang (2023), and Planck Collaboration et al. (2016) dust maps, jointly sampling the extinction coefficient.
Model Comparison: Bayesian evidence is calculated using the harmonic estimator to compare isotropic models against anisotropic models (odds ratios). For high-dimensional SN posteriors where evidence calculation is infeasible, the significance of the dipole amplitude is assessed via posterior distributions.

Key Results

CF4 TFR Sample: The analysis infers a zero-point dipole amplitude of $0.087 \pm 0.019$ mag. When expressed as a dipole in $H_0$ , this corresponds to an anisotropy of $4.1 \pm 0.9$ per cent. The Bayesian evidence strongly favors the anisotropic model over the isotropic one, with odds of 877:1 ( $\log B \approx 2.94$ ). This result is robust against variations in Galactic extinction corrections and prior choices.
Other TFR Samples: The 2MTF sample shows no significant dipole preference ( $\log B = -0.38$ ), while the SFI++ sample shows weak support for anisotropy ( $\log B = 0.47$ ). The authors attribute the lack of decisive evidence in these smaller samples to lower statistical power, confirmed by mock data analysis showing that sample sizes $>2000$ are required for decisive detection of a dipole of this magnitude.
Pantheon+ SNe: The SN data yields a zero-point dipole of $0.049 \pm 0.013$ mag ( $\sim 2.3 \pm 0.6$ per cent in $H_0$ ), which is significantly non-zero ( $>3.5\sigma$ ). However, Bayesian evidence could not be computed due to the high dimensionality of the posterior.
Bulk Flow Analysis (Crucial Finding): When the authors allow the external flow $V_{ext}$ to vary radially (rather than assuming a constant flow), the inferred flow magnitude rises initially but then rapidly decays to zero beyond $\sim 50 h^{-1}$ Mpc. This behavior is inconsistent with the linearly growing bulk flow expected from a true $H_0$ anisotropy. The resulting bulk flow curve is fully consistent with $\Lambda$ CDM expectations.
Mock Data Validation: Mock catalogues injected with a dipole of magnitude 0.087 mag confirm that the CF4 sample size ( $\sim 3200$ galaxies) is sufficient to yield "decisive" evidence ( $\log B > 2$ ), whereas smaller samples (like 2MTF) are not.

Significance and Claims
The paper claims that while there is a statistical preference for a dipole in the zero-point calibration of local distance tracers (specifically in the CF4 and Pantheon+ samples), this does not constitute evidence for a violation of the Cosmological Principle.

The authors argue that the apparent anisotropy is likely a manifestation of local peculiar velocities or systematics not fully captured by the standard C15 reconstruction, rather than a fundamental anisotropy in the expansion rate. Specifically:

Degeneracy Resolution: By allowing for a general, radially varying bulk flow, the model fits the data better than a model assuming a linearly growing flow (which would signal $H_0$ anisotropy). The preferred model yields a bulk flow consistent with $\Lambda$ CDM.
Systematic Robustness: The results are insensitive to the choice of Galactic extinction maps, suggesting the signal is not an artifact of dust correction.
Caveat on CP: The authors caution that because the analysis relies on the C15 reconstruction (which assumes the CP), any cosmological dipole present in the data might be partially absorbed by the reconstruction. However, given that the inferred bulk flow is consistent with $\Lambda$ CDM when modeled flexibly, the most plausible explanation is that the detected dipole reflects local flow features or systematics rather than a true cosmological anisotropy.

In conclusion, the study finds no evidence for a local $H_0$ anisotropy that violates the Cosmological Principle, attributing the observed dipole signals to the limitations of modeling local flows and the degeneracy between distance calibration and the Hubble constant.

The Big Question: Is the Universe "Fair"?

The Tools: Measuring the "Speed" of the Universe

The Investigation: The "Local Current" Problem

The Findings: A "False Alarm"

The Conclusion: The Ocean is Still Smooth

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