标题： 探索古老天体物理物体的年龄中的哈勃张力和空间曲率 显示英文标题

标题： Exploring the Hubble Tension and Spatial Curvature from the Ages of Old Astrophysical Objects

摘要： 我们使用红移范围为$0\lesssim z\lesssim 8$的 114 个古老天体物理对象 (OAO) 的年龄测量数据来探索哈勃矛盾。 宇宙在任何$z$的年龄与哈勃常数$H_0$成反比，因此要求宇宙在任何$z$的年龄大于其所包含的 OAO 的年龄将导致对$H_0$的上限。 假设平坦的$\Lambda$CDM，并对物质密度参数$\Omega_{\rm m}=0.315\pm0.007$设置由{\it 普朗克}提供信息的高斯先验，我们得到 95% 置信水平的上限为$H_0<70.6 \rm{~km} \rm{~s}^{-1} \rm{~Mpc}^{-1}$，这与使用本地距离阶梯测量的结果存在$2\sigma$的矛盾。 然而，我们发现推断出的$H_{0}$上限对$\Omega_{\rm m}$的先验假设非常敏感，早期和本地测量的$H_{0}$之间的哈勃矛盾可能部分是由于在{\it 普朗克}中同时推断了$\Omega_{\rm m}$和$H_0$，而本地测量仅使用了$H_{0}$。 年龄-红移数据也可用于宇宙学模型比较。 我们发现$R_{\rm h}=ct$宇宙能够很好地解释数据，对$H_{0}$有合理的上限，而爱因斯坦-德西特模型无法通过宇宙年龄测试。 最后，我们使用 61 个星系的年龄和 1,048 个潘顿 Ia 型超新星的光度距离，给出了一个与模型无关的空间曲率估计。 该分析表明，在置信水平为$1.6\sigma$的情况下，宇宙的几何结构与空间平坦性略有一致，表现为$\Omega_{k}=0.43^{+0.27}_{-0.27}$。 显示英文摘要

摘要： We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range $0\lesssim z\lesssim 8$ to explore the Hubble tension. The age of the Universe at any $z$ is inversely proportional to the Hubble constant, $H_0$, so requiring the Universe to be older than the OAO it contains at any $z$ will lead to an upper limit on $H_0$. Assuming flat $\Lambda$CDM and setting a Gaussian prior on the matter density parameter $\Omega_{\rm m}=0.315\pm0.007$ informed by {\it Planck}, we obtain a 95\% confidence-level upper limit of $H_0<70.6 \rm{~km} \rm{~s}^{-1} \rm{~Mpc}^{-1}$, representing a $2\sigma$ tension with the measurement using the local distance ladder. We find, however, that the inferred upper limit on $H_{0}$ depends quite sensitively on the prior for $\Omega_{\rm m}$, and the Hubble tension between early-time and local measurements of $H_{0}$ may be due in part to the inference of both $\Omega_{\rm m}$ and $H_0$ in {\it Planck}, while the local measurement uses only $H_{0}$. The age-redshift data may also be used for cosmological model comparisons. We find that the $R_{\rm h}=ct$ universe accounts well for the data, with a reasonable upper limit on $H_{0}$, while Einstein-de Sitter fails to pass the cosmic-age test. Finally, we present a model-independent estimate of the spatial curvature using the ages of 61 galaxies and the luminosity distances of 1,048 Pantheon Type Ia supernovae. This analysis suggests that the geometry of the Universe is marginally consistent with spatial flatness at a confidence level of $1.6\sigma$, characterized as $\Omega_{k}=0.43^{+0.27}_{-0.27}$.