Constraining Galaxy Cluster Triaxiality via Weak Lensing -- I. Preparation for the Rubin Data Beyond Leading Order

The 3D mass distributions of galaxy clusters are generally triaxial, a geometry that is difficult to constrain from projected observations. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It is relevant because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. In this work, we measure the projected halo shapes of clusters from their weak lensing signatures using the triaxiality functionality in the Cluster Lensing Mass Modeling. We measure ensemble halo ellipticity on the plane of the sky via axis-aligned stacking and multipole expansion of the weak lensing data.

We study a precursor dataset -- the redMaPPer cluster catalog, the metacalibration shape catalog, and the Directional Neighborhood Fitting photometric redshift catalog from the. We select clusters that have a high centering probability (>90%) of the identified central galaxy, and use the satellite galaxy distribution to determine the major-axis.

We extend the analysis to the second order of ellipticity in the monopole and quadrupole measurement. The projected ellipticity of the cluster sample is found to be $0.310^{+0.017}_{-0.016}$ (axis ratio $0.527^{+0.018}_{-0.019}$).

The projected cluster ellipticity shows no statistically significant dependence on mass and redshift. We further verify the accuracy of the cluster shape measurement using mock catalogs.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

This analysis is applicable to datasets from upcoming wide-area cosmic surveys such as LSST, Euclid, and the Roman Space Telescope, where larger sample sizes will lead to tighter. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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