AI 中文总结
该研究通过广义质量与视界关系导出修正宇宙学并进行限制，利用多种观测数据和马尔可夫链蒙特卡罗方法，对相关参数进行约束，虽能降低CMB - SH0ES张力，但未完全解决，且贝叶斯对数证据不支持相对于$\Lambda$CDM的扩展。
AI 中文摘要
我们对在论文I中从广义质量与视界关系（MHR）导出的修正宇宙学类别进行了限制，该关系强制蔡 - 金视界温度与广义视界熵之间的热力学一致性。修正的弗里德曼方程依赖于熵指数$m$、MHR耦合参数$\gamma$和纠缠修正幅度$f_B$，在适当极限下可恢复标准的$\Lambda$CDM。利用Pantheon + / SH0ES Ia型超新星、宇宙计时器、DESI DR2重子声学振荡和普朗克2018 CMB距离先验，我们通过马尔可夫链蒙特卡罗方法限制了八个具有物理动机的子情况，并通过贝叶斯对数证据比较模型。熵指数受到严格限制，当MHR耦合固定（$\gamma = 1$）时，$|m - 1|\lesssim O(10^{-4})$，沿$m - \gamma$简并性放宽到$O(10^{-3})$，排除了与标准视界热力学的任何宏观显著偏差。释放MHR耦合参数或纠缠幅度会将推断出的哈勃常数提高到$h\simeq0.70 - 0.71$，将CMB - SH0ES张力从${\sim}4\sigma$降低到${\sim}1.2 - 2.6\sigma$，但在平坦宇宙中没有任何情况能完全解决它。然而，在所有数据集组合中，贝叶斯对数证据都不支持相对于$\Lambda$CDM的每一种扩展（$-16\lesssim\Delta\ln Z \lesssim -1$）：当包括SH0ES校准时获得的改进拟合反映了额外参数对哈勃张力的吸收，而不是修正视界熵的真正证据。
英文摘要
We constrain the class of modified cosmologies derived in Paper I [1] from a generalized mass-to-horizon relation (MHR) that enforces thermodynamic consistency between the Cai-Kim horizon temperature and generalized horizon entropies. The modified Friedmann equations depend on an entropy exponent $m$, an MHR coupling parameter $γ$, and an entanglement-correction amplitude $f_B$, with standard $Λ$CDM recovered in the appropriate limit. Using Pantheon$+$/SH0ES Type~Ia supernovae, cosmic chronometers, DESI DR2 baryon acoustic oscillations, and Planck 2018 CMB distance priors, we constrain eight physically motivated sub-cases via Markov chain Monte Carlo and compare models through the Bayesian log-evidence. The entropy exponent is tightly bounded, $|m-1|\lesssim O(10^{-4})$ when the MHR coupling is fixed ($γ=1$), relaxing to $O(10^{-3})$ along the $m$-$γ$ degeneracy, excluding any macroscopically significant departure from standard horizon thermodynamics. Freeing the MHR coupling parameter or the entanglement amplitude raises the inferred Hubble constant to $h\simeq0.70$-$0.71$, reducing the CMB-SH0ES tension from ${\sim}4σ$ to ${\sim}1.2$-$2.6σ$, but no scenario fully resolves it within a flat universe. The Bayesian log-evidence nevertheless disfavors every extension relative to $Λ$CDM in all dataset combinations ($-16\lesssimΔ\ln Z \lesssim-1$): the improved fits obtained when the SH0ES calibration is included reflect an absorption of the Hubble tension by the additional parameters rather than genuine evidence for modified horizon entropy.
Comments14 pages, 4 figures, 7 tables
