哈勃张力：形状墙
Hubble tension: the shape wall
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中文总结 AI 辅助
研究哈勃张力后期解决方案，指出标准‘不可行定理’是归一化墙。后期解决方案受BAO归一化及膨胀历史形状约束，利用高斯过程等对\(E(z)\)非参数重建量化‘形状墙’，最保守分析发现\(H_0\)最大分数增加远低于解决张力所需，限制了后期修改对\(H_0\)的增加量。
中文摘要 AI 辅助
针对哈勃张力后期解决方案的标准‘不可行定理’本质上是一个归一化墙，因为重子声学振荡（BAO）测量约束了乘积\(H_0r_d\)，其中\(r_d\)是重子拖曳时的声视界。后期解决方案（保持\(r_d\)固定）不仅受到BAO归一化\(H_0r_d\)的严格约束，还受到膨胀历史形状的约束，即无量纲膨胀率\(E(z) \equiv H(z)/H_0\)。研究表明，若\(r_d\)和声角尺度\(\theta_s\)固定，\(H_0\)的增加需要由无量纲距离积分\(I \equiv \int dz/E(z)\)的同等分数增加来匹配：\(\delta H_0/H_0 \simeq \delta I/I\)。利用高斯过程以及最新的无锚定Ia型超新星（SNeIa）和BAO数据对\(E(z)\)进行非参数重建，以量化由\(E(z)\)的相对距离约束设置的‘形状墙’。在最保守分析中，使用PantheonPlus SNeIa和DESI DR2 BAO数据，发现\(H_0\)的最大分数增加\(\lesssim 2\%\)，远低于解决张力所需的\(\gtrsim 8\%\)。此形状墙即使在存在早期新物理的情况下也成立，限制了在固定\(\theta_s\)时由\(E(z)\)的后期修改对\(H_0\)的最大增加量。所以，后期修改无论是单独调用还是与早期新物理一起，不仅面临众所周知的归一化墙，还面临严格的百分比级形状墙。
英文摘要
The standard "no-go theorem" against late-time solutions to the Hubble tension is essentially a normalization wall, since Baryon Acoustic Oscillation (BAO) measurements constrain the product $H_0r_d$, with $r_d$ the sound horizon at baryon drag. However, late-time solutions (which keep $r_d$ fixed) are tightly constrained not only by the BAO normalization $H_0r_d$, but also by the shape of the expansion history, i.e. the dimensionless expansion rate $E(z) \equiv H(z)/H_0$. We show that, if $r_d$ and the acoustic angular scale $θ_s$ are fixed, an increase in $H_0$ needs to be matched by an equal fractional increase in the dimensionless distance integral $I \equiv \int dz/E(z)$: $δH_0/H_0 \simeq δI/I$. We use this to quantify the "shape wall" set by relative distance constraints on $E(z)$, which we reconstruct nonparametrically, using Gaussian Processes and the latest unanchored Type Ia Supernovae (SNeIa) and BAO data. In our most conservative analysis using PantheonPlus SNeIa and DESI DR2 BAO data, we find a maximum fractional increase in $H_0$ of $\lesssim 2\%$, falling well short of the $\gtrsim 8\%$ required to solve the tension. This shape wall holds even in the presence of early-time new physics, and limits the maximum increase in $H_0$ which can be contributed by late-time modifications to $E(z)$ at fixed $θ_s$. Therefore, late-time modifications, whether invoked alone or alongside early-time new physics, face not only the well-known normalization wall, but also a stringent percent-level shape wall.
发表机构
- University of Trento（特伦托大学）
- Trento Institute for Fundamental Physics and Applications (TIFPA)-INFN（特伦托基础物理与应用研究所（TIFPA）-意大利国家核物理研究所）
- Istanbul Technical University（伊斯坦布尔理工大学）
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