信息几何视角下的哈勃张力：wCDM模型中的本征模式旋转与曲率抑制
Information-Geometric Perspective on the Hubble Tension: Eigenmode Rotation and Curvature Suppression in wCDM
AI总结：
本文从信息几何角度分析wCDM模型中哈勃张力的来源，通过分解参数位移与方向 Fisher 曲率，揭示扩展ΛCDM模型对CMB约束几何的影响，显示高精度晚期数据增强了膨胀率方向的曲率，从而抑制了伪暗能量逃逸路径。
摘要：
哈勃张力不仅由早期和晚期参数估计之间的差异塑造，还受到定义这些估计的约束刚性的刚性影响。本文在wCDM模型中分析这一几何结构，将差异分解为参数位移和方向Fisher曲率。在局部高斯近似下，给定方向上的二次张力分解为平方位移和由数据集贡献的结合方向曲率。将此框架应用于普朗克、DESI DR2和SH0ES数据，显示扩展ΛCDM到wCDM主要重塑CMB约束的Fisher几何而非开辟新路径。允许暗能量方程状态参数w变化使普朗克Fisher本征值降低至ΛCDM值的约2.7%，同时产生主导声学尺度本征模式的适度旋转。净效应是有效声学刚性的显著软化。同时，高精度晚期数据，尤其是DESI DR2，注入了膨胀率方向的显著曲率。此增加的刚性作为几何墙，关闭了伪暗能量逃逸路径，并在扩展参数空间内显著限制张力缓解。本文结果表明，模型扩展下推导的H_0张力变化应理解为约束流形的重新配置而非新物理证据。位移-曲率分解因此提供了一种简单、快速且物理透明的诊断宇宙学张力的方法。
英文摘要：
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.
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