AI 中文总结
研究哈勃张力问题，通过通用框架比较14种替代ΛCDM模型的方案，用频率主义和贝叶斯方法评估，发现早期暗能量和早期修正引力模型表现最佳，能减小残余差异，为解决哈勃张力提供了重要参考。
AI 中文摘要
哈勃张力已达到名义上高于7σ的显著水平，而宇宙微波背景（CMB）和重子声学振荡（BAO）的新高精度测量使对所提解决方案的检验更加严格。我们使用通用框架，根据最新的CMB、BAO和超新星数据，比较了14种有代表性的替代标准Λ冷暗物质（ΛCDM）模型的方案，以评估它们解决该张力的能力。这些模型涵盖晚期修正、修正复合以及由额外辐射或局部暗能量注入驱动的奇异复合前膨胀历史。我们用互补的频率主义和贝叶斯方法评估每个方案的残余校准张力和联合拟合的改善情况。两种方法都确定了相同的大致层次结构。早期暗能量和早期修正引力模型表现最佳，在无局部测量先验的情况下将哈勃常数推断值移向70 km s⁻¹ Mpc⁻¹，并将与SH0ES的残余差异减小到约2.5 - 3.6σ，具体取决于模型和统计量，且在联合拟合中比ΛCDM获得更强支持。重组时改变电子质量有中等程度改善，而增强辐射和晚期情景未比ΛCDM有改进。本文总结了竞赛的小组赛阶段；在一篇配套论文（论文II）中，我们展示了详尽分析的结果，并评估了它们对建模假设和数据集变化的稳健性。
英文摘要
The Hubble tension has reached a nominal significance above $7σ$, while new high-precision measurements of the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) sharpen the test of proposed solutions. Using a common framework, we compare fourteen representative alternatives to the standard $Λ$ Cold Dark Matter ($Λ$CDM) model in light of up-to-date CMB, BAO and supernovae data to gauge their ability to resolve the tension. The models span late-time modifications, modified recombination, and exotic pre-recombination expansion histories driven by additional radiation or a localized dark energy injection. We evaluate each proposal with complementary frequentist and Bayesian measures of the residual calibration tension and of the improvement in the joint fit. Both approaches identify the same broad hierarchy. Early dark energy and early modified gravity models perform best, shifting the $H_0$ inference without local measurement priors toward $70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and reducing the residual discrepancy with SH0ES to approximately $2.5-3.6σ$, depending on the model and statistic, while receiving strong support over $Λ$CDM in the combined fit. Varying the electron mass at recombination yields an intermediate improvement, whereas the enhanced-radiation and late-time scenarios do not improve over $Λ$CDM. This Letter summarizes the group stage of the competition; in a companion paper (Paper II) we present the results of an exhaustive set of analyses and assess their robustness to variations in modeling assumptions and datasets.
Comments8 pages, 1 figure, 1 table
