Galaxy Clusters Reveal Hints of Cosmic Anisotropy, but the Universe Refuses to Break Its Symmetry Just Yet

The cosmological principle is the quiet assumption underneath nearly everything cosmologists believe about the universe: that on sufficiently large scales, matter is spread out evenly and no direction in the sky is special. Every calculation in the standard Lambda cold dark matter model, from the age of the universe to the growth of cosmic structure, leans on that assumption. Now a team of researchers has put it to one of its most careful tests yet, using a large sample of galaxy clusters observed in X-rays and a statistical technique called the dipole fitting method, which had never before been applied to this kind of data. Their conclusion is subtle: there are hints of anisotropy, a faint directional pattern in how galaxy clusters shine, but the signal falls well short of the statistical strength needed to declare that the universe has a preferred direction.

The study, published in The European Physical Journal C, was led by J. P. Hu and colleagues, who analyzed a catalog of 313 galaxy clusters drawn from the Meta-Catalogue of X-ray detected Clusters of galaxies. The clusters were originally compiled by Migkas and collaborators and all have high-quality public observations from either the Chandra X-ray Observatory or the XMM-Newton space telescope. The sample spans redshifts from 0.004 to 0.447, meaning it reaches back across billions of years of cosmic history. Crucially, compared with the type Ia supernovae that cosmologists usually use to probe anisotropy, galaxy clusters are distributed far more evenly across the sky. Supernova catalogs such as Pantheon and Pantheon+ contain dense bands of observations, notably from the Sloan Digital Sky Survey, and that uneven coverage can artificially inflate the apparent significance of anisotropy measurements. Galaxy clusters, by contrast, offer a spatial distribution that makes them a cleaner probe of whether the universe truly looks the same in every direction.

The physical heart of the analysis is the relationship between the X-ray luminosity of a galaxy cluster and the temperature of its hot gas. Galaxy clusters are the most massive gravitationally bound structures in existence, and roughly ten percent of their mass sits in an intracluster medium, a seething reservoir of plasma at tens of millions of degrees that pours out X-rays. Theory predicts, and observations confirm, that X-ray luminosity and gas temperature follow a tight power-law scaling relation. Because a cluster’s measured X-ray flux must be converted into a luminosity using its luminosity distance, which itself depends on the assumed cosmological model, any directional variation in this relation could betray either a genuine anisotropy in the universe or a systematic effect in the data. The team fitted the scaling relation with a normalization parameter k, a slope s, and an intrinsic scatter term, using a flat Lambda cold dark matter cosmology with a matter density of 0.30, a dark energy density of 0.70, and a Hubble constant of 70.0 kilometers per second per megaparsec.

The dipole fitting method, originally developed to search for tiny variations in the fine structure constant, works by adding a directional correction to the expected luminosity of each cluster. The correction takes the form of a dipole, the first two terms of a spherical harmonic expansion, described by four parameters: the galactic longitude l and latitude b of a preferred axis, a dipole magnitude A, and a monopole term B. If the universe is isotropic, both A and B should be consistent with zero. A negative value of A means clusters in that direction are dimmer than the standard scaling relation predicts at a given temperature, and the direction associated with the negative dipole is taken as the preferred direction of any anisotropy. The team fitted seven parameters in total, using a Bayesian Markov chain Monte Carlo approach with the emcee package, running 300 walkers for 5000 steps each and discarding the first 50 steps as burn-in.

For the full combined sample of 313 clusters, the analysis pointed to a preferred direction at galactic coordinates of longitude 257.82 degrees and latitude minus 31.30 degrees, with uncertainties of roughly 50 to 60 degrees, and a dipole magnitude of A equal to minus 5.4 times ten to the minus four, with an uncertainty of 6.3 times ten to the minus four. That central value is tiny, and the uncertainty is larger than the value itself, which already signals that the detection is marginal. The team also found the mirror-image solution, as the dipole model always produces two nearly symmetric directions, one brighter and one darker, and only the darker one is treated as the preferred direction. When they repeated the analysis while simultaneously fitting the scaling relation parameters rather than fixing them, the preferred direction barely moved, confirming that the choice of how to handle the luminosity-temperature relation has only a weak effect on the anisotropy result, even though the normalization parameter k and the monopole term B are strongly coupled and cannot be constrained at the same time.

The more troubling finding emerged when the sample was split by instrument. The Chandra dataset, containing 237 clusters over a wider redshift range, gave a dipole magnitude of only minus 1.9 times ten to the minus four and a preferred direction at longitude 328.31 degrees. The XMM-Newton dataset, with just 76 clusters, yielded a much stronger signal of minus 32.0 times ten to the minus four and pointed in a completely different direction, at longitude 184.42 degrees. The difference in preferred longitude between the two instruments is a striking 143.89 degrees. The two instruments also disagreed on the slope of the luminosity-temperature relation itself, with a discrepancy in the slope parameter s reaching 4.01 sigma. The authors note that these differences could stem from real physical variation, instrumental calibration effects, sample selection, or the different redshift coverage and sky distribution of the two datasets, and that at present it is impossible to determine which explanation is correct.

Redshift added another layer of complexity. Splitting the sample at redshift 0.10 produced a low-redshift group of 219 clusters and a high-redshift group of 94. The normalization parameter k differed between the two groups by 0.88, a 5.18 sigma discrepancy, hinting that the luminosity-temperature relation itself may evolve with cosmic time. The high-redshift subsample also produced a stronger anisotropy signal, with a dipole magnitude of minus 16.2 times ten to the minus four, and a preferred direction far from that of the low-redshift group. The authors caution that when anisotropy is probed through spatial variations of the luminosity-temperature relation, differences in the redshift distribution of data across the sky can masquerade as genuine anisotropies, contaminating the detected signal.

To judge whether the measured dipole was anything more than noise, the team built a statistical isotropy framework tailored to the dipole fitting method, running 1000 simulated datasets under two schemes. In the Bootstrap scheme, the observed values were randomly reshuffled among the real cluster positions, preserving the sky coverage while destroying any physical anisotropy. In the Randomized scheme, the data points were redistributed uniformly across the celestial sphere. The simulated dipole magnitudes all fell between minus and plus ten to the minus three, and the real value exceeded the simulated expectation. Under the Bootstrap scheme, the statistical significance of the real signal was 0.2 sigma for Chandra, 1.8 sigma for XMM-Newton, and 0.6 sigma for the combined sample; under the Randomized scheme the corresponding figures were 0.3, 1.9, and 0.6 sigma. The low- and high-redshift subsamples reached 0.6 and 1.7 sigma under Bootstrap and 0.7 and 1.8 sigma under Randomized. The fact that the two schemes gave similar answers suggests the anisotropy is not primarily an artifact of uneven sky coverage, and the authors interpret this as indicating the signal, if real, is more likely contributed by the non-uniformity of cosmic structure itself, though other factors within the cluster data may contribute at a comparable level.

A controlled comparison sharpened the instrument puzzle. The team generated 200 Chandra subsamples matched to the XMM-Newton sample in both size and redshift distribution using importance sampling. With sample composition effects largely removed, the preferred directions detected by the two instruments converged, but the anisotropy strength did not: the XMM-Newton data still showed a markedly stronger signal. This points away from sample composition alone and toward either genuine physical differences or systematic effects tied to the instruments or data processing, a question the study leaves open. The matched Chandra subsamples yielded a mean dipole magnitude of minus 4.4 times ten to the minus four and a mean preferred longitude of 214.34 degrees.

How does this stack up against earlier work? Using a sky-scanning method on the same cluster sample, Migkas and collaborators had reported anisotropy toward galactic coordinates 280 degrees, minus 20 degrees at a confidence level of at least 4 sigma. The new dipole fitting result, pointing at 257.82 degrees, minus 31.30 degrees, is consistent with that direction within 1.49 sigma when one-sided errors are considered, but the significance the new method assigns to the signal, around 0.6 sigma for the combined sample, is dramatically weaker. The preferred directions from the XMM-Newton and high-redshift subsets also disagree with the directions reported from the cosmic microwave background dipole, bulk flows, gamma-ray bursts, and supernova catalogs, though the authors stress that comparing directions across probes covering different redshift ranges and with wildly different significances has serious limitations. The bottom line of the study is measured: anisotropic signals are present in the galaxy cluster data, but they do not reach the statistical confidence needed to challenge the cosmological principle. The team points to future high-quality cluster observations from the e-ROSITA X-ray survey as the path toward confirming or refuting these faint directional whispers from the largest structures in the universe.

Subject of Research: Testing the cosmological principle with X-ray galaxy clusters using the dipole fitting method

Article Title: Probing cosmic anisotropy from galaxy clusters via the dipole fitting method

Article References: Hu, J. P., Geng, C., Jia, X. D., Zuo, Z. Y., Yang, T. Z., & Wang, F. Y. (2026). Probing cosmic anisotropy from galaxy clusters via the dipole fitting method. The European Physical Journal C, 86(10), Article 1207. https://doi.org/10.1140/epjc/s10052-026-16365-w

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16365-w

Keywords: cosmological principle, cosmic anisotropy, galaxy clusters, dipole fitting method, X-ray luminosity-temperature relation, Chandra, XMM-Newton, Lambda cold dark matter, Hubble tension, statistical isotropy, e-ROSITA, cosmology