Information-Geometric Perspective on the Hubble Tension: Eigenmode Rotation and Curvature Suppression in wCDM

TL;DR

This paper introduces a geometric framework to analyze the Hubble tension in cosmology, revealing how model extensions reshape constraint geometry and influence tension without implying new physics.

Contribution

It develops a shift-curvature decomposition method to diagnose cosmological tensions, applied to wCDM model and datasets, highlighting geometric effects over physical changes.

Findings

Extending b3CDM reshapes Fisher geometry more than opening new routes to concordance.

Allowing w to vary suppresses Planck Fisher eigenvalue to rac{2.7}{100} of its b3CDM value.

High-precision late-time data injects curvature, limiting tension relief within extended models.

Abstract

The Hubble tension is shaped not only by shifts between early- and late-time parameter estimates, but also by the stiffness of the constraints that define them. In this work, we analyze this geometric structure in the wCDM model by separating the discrepancy into two components: a parameter displacement and a directional Fisher curvature. Within the local Gaussian approximation, the quadratic tension along a given direction factorizes into the squared shift and the combined directional curvature contributed by the datasets. Applying this framework to Planck, DESI DR2, and SH0ES, we show that extending \LambdaCDM to wCDM primarily reshapes the Fisher geometry of the CMB constraint rather than opening a genuinely new route to concordance. Allowing the dark-energy equation-of-state parameter w to vary suppresses the leading Planck Fisher eigenvalue to only \sim 2.7 % of its \LambdaCDM value, while producing only a modest rotation of the dominant acoustic-scale eigenmode. The net effect is a strong softening of the effective acoustic rigidity. At the same time, high-precision late-time data, especially from DESI DR2, inject substantial curvature along the expansion-rate direction. This added stiffness acts as a geometric wall, closing off phantom-like escape routes and sharply limiting tension relief within the extended parameter space. Our results indicate that changes in the inferred H_0 tension under model extension are best understood as a reconfiguration of the constraint manifold rather than as evidence for new physical agreement. The shift-curvature decomposition thus offers a simple, fast, and physically transparent way to diagnose cosmological tensions.