Recently, two classes of quasar samples were identified, which are promising as new cosmological probes extending to higher redshifts. The first sample uses the nonlinear relation between the ultraviolet and X-ray luminosities of quasars to derive luminosity distances, whereas the linear sizes of compact radio quasars in the second sample can serve as standardized rulers, providing angular-diameter distances. In this study, under the assumption of a flat universe, we refreshed the calibration of multiple measurements of high-redshift quasars (in the framework of a cosmological-model-independent method with the newest Hubble parameters data). Furthermore, we placed constraints on four models that characterize the cosmic equation of state (w). The obtained results show that: (1) the two quasar samples could provide promising complementary probes at much higher redshifts, whereas compact radio quasars perform better than ultraviolet and X-ray quasars at the current observational level; (2) strong degeneracy between the cosmic equation of state (w) and Hubble constant (H₀) is revealed, which highlights the importance of independent determination of H₀ from time-delay measurements of strongly lensed quasars; (3) together with other standard ruler probes, such as baryon acoustic oscillation distance measurements, the combined QSO+BAO measurements are consistent with the standard ΛCDM model at a constant equation of state w = −1; (4) ranking the cosmological models, the polynomial parametrization gives a rather good fit among the four cosmic-equation-of-state models, whereas the Jassal-Bagla-Padmanabhan (JBP) parametrization is substantially penalized by the Akaike Information Criterion and Bayesian Information Criterion.

最近，确定了两类类星体样品，它们有望作为新的宇宙学探针扩展到更高的红移。第一个样本使用类星体的紫外线和X射线光度之间的非线性关系来得出光度距离，而第二个样本中的紧凑型无线电类星体的线性大小可以用作标准化的标尺，提供角直径距离。在这项研究中，在一个平坦宇宙的假设下，我们刷新了高红移类星体的多次测量的校准（在具有最新哈勃参数数据的独立于宇宙论模型的方法的框架内）。此外，我们在表征宇宙状态方程（w）。得到的结果表明：（1）这两个类星体样品可以在更高的红移下提供有希望的互补探针，而在目前的观测水平上，紧凑型射电类星体的性能优于紫外线和X射线类星体；（2）揭示了宇宙状态方程（w）和哈勃常数（H ₀）之间的强简并性，这突出了从强透镜类星体的时延测量中独立确定H ₀的重要性；（3）与其他标准尺探针（例如重子声振荡距离测量）一起，在状态常数为w的情况下，组合的QSO + BAO测量与标准ΛCDM模型一致= -1; （4）在对宇宙学模型进行排名时，多项式参数化在四个宇宙方程状态模型中具有很好的拟合度，而Jassal-Bagla-Padmanabhan（JBP）的参数化受到Akaike信息准则和贝叶斯信息的严重惩罚标准。