AI 中文总结
该研究通过改进的\texttt{CLASS}求解器结合多组观测数据约束WGB拓扑暗能量，发现其可部分缓解$H_0$张力，同时揭示$H_0$与$S_8$的特征权衡关系。
AI 中文摘要
持续存在的$H_0$（哈勃常数）和$S_8$（结构涨落振幅）张力，促使人们寻找能够修改宇宙晚期膨胀历史、同时保留$\rm{\u039A}CDM$（冷暗物质+宇宙学常数模型）对早期宇宙成功预测的新型暗能量机制。Wald-Gauss-Bonnet（WGB）拓扑暗能量为这种可能性提供了具有物理动机的实现方式，其有效暗能量部分源自宇宙视界热力学以及黑洞形成与并合历史。我们首次开展WGB宇宙学的早期与晚期宇宙分析，将该模型作为有效流体纳入改进后的\texttt{CLASS}求解器，并利用来自Planck、ACT DR6、SPT-3G的CMB（宇宙微波背景）数据、DESI DR2 BAO（重子声学振荡）数据以及Pantheon+超新星数据对其进行约束。仅晚期数据与$\rm{\u039A}CDM$模型一致，而完整数据集倾向于非零的WGB贡献，$\tilde{C}_n=0.435^{+0.150}_{-0.132}$，对应约$3\tilde{\u03C3}$的类幻影偏差且拟合效果得到改善。该偏好解将$H_0$从$68.5$提升至$69.8\rm{\u00A0km/s/Mpc}$，使哈勃张力降低约$0.9\tilde{\u03C3}$，代价是$S_8$略有上升。重建的宇宙学可观测量显示，WGB几乎不改变初级CMB，却增强了引力透镜效应与小尺度成团性，揭示出$H_0$-$S_8$之间的特征权衡关系。因此，WGB暗能量成为一种具有物理动机且观测上可行的晚期机制，可在不引入新的早期宇宙物理的情况下部分缓解哈勃张力。
英文摘要
The persistent $H_0$ and $S_8$ tensions motivate the search for new dark-energy mechanisms capable of modifying the late-time expansion history while preserving the successful early-Universe predictions of $Λ$CDM scenario. Wald-Gauss-Bonnet (WGB) topological dark energy provides a physically motivated realization of this possibility, where the effective dark-energy sector emerges from cosmic horizon thermodynamics and the black-hole formation and merger history. We present the first early- and late-Universe analysis of WGB cosmology, implementing the model as an effective fluid in a modified \texttt{CLASS} solver and constraining it against CMB data from \textit{Planck}, ACT~DR6 and SPT-3G, DESI~DR2 BAO, and Pantheon+ supernovae. While late-time data alone are consistent with $Λ$CDM, the full dataset prefers a non-zero WGB contribution, $\Cn=0.435^{+0.150}_{-0.132}$, corresponding to a $\sim3σ$ phantom-like deviation and an improved fit. The preferred solution raises $H_0$ from $68.5$ to $69.8~\kmsmpc$, reducing the Hubble tension by $\sim0.9σ$, at the cost of a mild increase in $S_8$. The reconstructed cosmological observables show that WGB leaves the primary CMB almost unchanged while enhancing lensing and small-scale clustering, revealing a characteristic $H_0$-$S_8$ trade-off. WGB dark energy therefore emerges as a physically motivated and observationally viable late-time mechanism for partially alleviating the Hubble tension without introducing new early-Universe physics.
Comments19 pages, 9 figures
