Although the Hubble constant H0 and spatial curvature ΩK have been measured with very high precision, they still suffer from some tensions. In this paper, we propose an improved method to combine the observations of ultracompact structure in radio quasars and strong gravitational lensing with quasars acting as background sources to determine H0 and ΩK simultaneously. By applying the distance sum rule to the time-delay measurements of seven strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers, we obtain stringent constraints on the Hubble constant (H0 = 78.3 ± 2.9 km s−1 Mpc−1) and the cosmic curvature (ΩK = 0.49 ± 0.24). On the one hand, in the framework of a flat universe, the measured Hubble constant ($H_0=73.6^{+1.8}_{-1.6} \mathrm{\,km\,s^{-1}\,Mpc^{-1}}$) is strongly consistent with that derived from the local distance ladder, with a precision of 2 per cent. On the other hand, if we use the local H0 measurement as a prior, our results are marginally compatible with zero spatial curvature ($\Omega _K=0.23^{+0.15}_{-0.17}$) and there is no significant deviation from a flat universe. Finally, we also evaluate whether strongly lensed quasars would produce robust constraints on H0 and ΩK in the non-flat and flat Λ cold dark matter model, if the compact radio structure measurements are available from very long baseline interferometry observations.

中文翻译：

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用类星体测量哈勃常数和宇宙曲率：超紧凑无线电结构和强引力透镜

虽然哈勃常数 H0 和空间曲率 ΩK 的测量精度非常高，但它们仍然存在一些张力。在本文中，我们提出了一种改进的方法，将射电类星体中超致密结构的观测和强引力透镜与作为背景源的类星体相结合，同时确定 H0 和 ΩK。通过将距离和规则应用于七个强透镜系统和 120 个作为标准标尺校准的中等光度类星体的时间延迟测量，我们获得了对哈勃常数的严格约束（H0 = 78.3 ± 2.9 km s-1 Mpc-1）和宇宙曲率（ΩK = 0.49 ± 0.24）。一方面，在平坦宇宙的框架下，测得的哈勃常数($H_0=73.6^{+1.8}_{-1.6}\mathrm{\,km\,s^{-1}\, Mpc^{-1}}$) 与从局部距离阶梯推导出的结果高度一致，精度为 2%。另一方面，如果我们使用局部 H0 测量作为先验，我们的结果与零空间曲率（$\Omega _K=0.23^{+0.15}_{-0.17}$）略微兼容，并且没有显着偏差来自一个平坦的宇宙。最后，我们还评估了强透镜类星体是否会对非平坦和平坦 Λ 冷暗物质模型中的 H0 和 ΩK 产生稳健的约束，如果可以从非常长的基线干涉测量观测中获得紧凑的无线电结构测量结果。17}$) 并且与平坦宇宙没有显着偏差。最后，我们还评估了强透镜类星体是否会对非平坦和平坦 Λ 冷暗物质模型中的 H0 和 ΩK 产生稳健的约束，如果可以从非常长的基线干涉测量观测中获得紧凑的无线电结构测量结果。17}$) 并且与平坦宇宙没有显着偏差。最后，我们还评估了强透镜类星体是否会对非平坦和平坦 Λ 冷暗物质模型中的 H0 和 ΩK 产生稳健的约束，如果可以从非常长的基线干涉测量观测中获得紧凑的无线电结构测量结果。