引力透镜是研究宇宙学的一种强有力探针，其应用不仅限于探索暗物质分布，还包括研究宇宙中的其他重要问题。随着观测技术的不断进步，星系团尺度的强引力透镜系统也不断增多，成为宇宙学研究中的独特工具。同时，类星体作为宇宙中最亮的天体之一，一直被视为宇宙标准烛光的潜在候选体。特别是，通过构建多波段（$L_X-L_{UV}$）类星体的高红移哈勃图，可以为宇宙学研究提供新的手段。
本文以星系团强引力透镜和多波段类星体作为新探针，结合超新星标准烛光、哈勃参数标准时钟以及引力波标准汽笛，旨在研究宇宙学中存在的不一致问题，尤其关注哈勃常数危机、宇宙曲率测量、可变光速以及标准宇宙学模型$\Lambda$CDM的有效性问题，以期寻找可能指向新物理的证据。
首先，哈勃常数作为宇宙学中重要参数之一，目前正经历着一场严重的危机。本文中，研究了基于星系团透镜化类星体系统的时间延迟限制哈勃常数的独立方法，该方法与透镜化多重像的时间延迟和星系团透镜建模有关。具体来说，聚焦于2003年发现的第一个星系团透镜化类星体SDSS J1004+4112系统。该系统包括5个透镜化类星体图像和27个透镜化背景星系图像，并且拥有历经多年直至2022年才观测到的最长的时间延迟（约3600天）。
结合SDSS J1004+4112系统的最新观测，构建了16种透镜模型，得到的哈勃常数为$H_0=67.5^{+14.5}_{-8.9}\mathrm{~km~s^{-1}~Mpc^{-1}}$。并且，发现不同透镜模型之间存在强烈的依赖性，这可能是由于SDSS J1004+4112系统的多重像数目不够多，不足以打破对大质量星系团透镜模型的依赖。因此，又聚焦于2014年发现的第一个可分辨多重像的星系团透镜化超新星SN Refsdal系统。该系统包括6个透镜化超新星图像和103个透镜化背景星系图像，并且直至2023年才观测到超新星的第五个像的时间延迟（约为370多天）。结合SN Refsdal系统的最新观测，构建了23种透镜模型，得到的哈勃常数为$H_0=70.0^{+4.7}_{-4.9}\mathrm{~km~s^{-1}~Mpc^{-1}}$。并且，发现不同透镜模型之间的依赖性很弱。相较于SDSS J1004+4112系统，得到了更为严格的哈勃常数，可以在一定程度上缓解哈勃常数危机。
同时，宇宙曲率测量也随着哈勃常数危机的出现而显现。
本文中，研究了基于多波段类星体高红移哈勃图限制宇宙曲率的独立方法，该方法与光度距离$D_L(z)$和哈勃参数$H(z)$有关。具体来说，聚焦于2019年构建的多波段（$L_X-L_{UV}$）类星体高红移哈勃图。该样本包括1598个类星体，红移高达5.1。结合宇宙计时器标准时钟得到的哈勃参数$H(z)$，得到了不同红移处宇宙曲率的值，统计学意义下的宇宙曲率为$\Omega_k=0.08\pm0.31$。这意味着，在目前观测水平下，支持一个平坦的宇宙。
有人认为哈勃常数危机和宇宙曲率测量出现的原因可能是标准宇宙学模型$\Lambda$CDM失效。
因此，需要检验$\Lambda$CDM的有效性。在直接检验$\Lambda$CDM的有效性之前，本文研究了光速的不变性，间接检验广义相对论，然后进一步检验$\Lambda$CDM。
具体来说，研究了基于多波段类星体高红移哈勃图限制光速的独立方法，该方法也是只与$D_L(z)$和$H(z)$有关。对于多波段类星体哈勃图提供的$D_L(z)$和宇宙计时器标准时钟提供的$H(z)$，
得到了不同红移处变光速参数$\eta\equiv c/c_0$的值，统计学意义下的限制结果为$\eta=1.19\pm0.07$，没有强烈证据偏离恒定值$\eta=1$。
最后，
研究了检验标准宇宙学模型$\Lambda$CDM有效性的两点诊断$Omh^2$方法，
该方法只与$H(z)$有关。
为了保证检验的模型独立性，只考虑宇宙计时器标准时钟得到的哈勃参数$H(z)$。该样本包括33个$H(z)$测量值，红移最高到2.0。
得到了不同红移处$Omh^2$的值，加权平均统计学分析下的结果为$Omh^2=0.1438\pm0.0045$，
与普朗克2018年的限制结果$0.1428\pm0.0011$一致。
并且，与宇宙学模型$\omega$CDM和CPL模型相比，$\Lambda$CDM模型在两点诊断$Omh^2$方法下表现更好。
总之，本文以星系团强引力透镜和多波段类星体为主要宇宙学新型探针，研究了哈勃常数、宇宙曲率、光速不变性和标准宇宙学有效性等宇宙学热点问题，在目前观测水平下，虽然没有发现新物理的证据，但是得到了一些有创新型的有趣结论。随着未来观测的不断发展，可能揭示出新的物理规律。

Gravitational lensing is a powerful probe for studying cosmology, with applications not only limited to exploring the distribution of dark matter but also encompassing the investigation of other significant issues in the universe. With the continuous advancement of observational techniques, the number of strong gravitational lensing systems at the scale of galaxy clusters has been increasing, making them unique tools in cosmological research. Meanwhile, quasars, as one of the brightest objects in the universe, have long been considered as potential candidates for cosmological standard candles. In particular, constructing high-redshift Hubble diagrams of quasars in multiple bands ($L_X-L_{UV}$) can provide new means for cosmological studies.
This paper takes galaxy cluster strong gravitational lensing and multi-band quasars as new probes, combining standard candles of supernovae, the Hubble parameter standard clock, and gravitational wave standard sirens to study inconsistencies in cosmology, especially focusing on the Hubble crisis, the curvature tension, variable speed of light, and the effectiveness of the standard cosmological model $\Lambda$CDM, in the hope of finding evidence that may point to new physics.
Firstly, the Hubble constant, as one of the important parameters in cosmology, is currently undergoing a serious crisis. In this paper, an independent method based on time delay from galaxy cluster lensed quasar systems is studied to constrain the Hubble constant, which is related to time delays of lensed multiple images and galaxy cluster lens modeling. Specifically, attention is focused on the SDSS J1004+4112 system, the first galaxy cluster lensed quasar system discovered in 2003. The system includes 5 lensed quasar images and 27 lensed background galaxy images, with the longest time delay observed until 2022 being approximately 3600 days. By combining the latest observations of the SDSS J1004+4112 system, 16 lens models are constructed, yielding a Hubble constant of $H_0=67.5^{+14.5}_{-8.9}\mathrm{~km~s^{-1}~Mpc^{-1}}$. It is found that there is strong dependence among different lens models, possibly due to insufficient number of lensed images in the SDSS J1004+4112 system to break the degeneracy among massive galaxy cluster lens models. Therefore, attention is then directed to the SN Refsdal system, the first galaxy cluster lensed supernova system with resolvable multiple images discovered in 2014. The system includes 6 lensed supernova images and 103 lensed background galaxy images, with the time delay of the fifth image observed until 2023 being approximately 370 days. By combining the latest observations of the SN Refsdal system, 23 lens models are constructed, yielding a Hubble constant of $H_0=70.0^{+4.7}_{-4.9}\mathrm{~km~s^{-1}~Mpc^{-1}}$. It is found that there is weak dependence among different lens models. Compared to the SDSS J1004+4112 system, a more stringent Hubble constant is obtained, which may alleviate the Hubble crisis to some extent.
Meanwhile, the curvature tension also emerges with the appearance of the Hubble crisis. In this paper, an independent method based on high-redshift Hubble diagrams of multi-band quasars is studied to constrain the curvature of the universe, which is related to luminosity distance $D_L(z)$ and the Hubble parameter $H(z)$. Specifically, attention is focused on the multi-band ($L_X-L_{UV}$) quasar high-redshift Hubble diagram constructed in 2019. The sample includes 1598 quasars with redshifts up to 5.1. By combining the Hubble parameter $H(z)$ obtained from cosmic chronometers, the values of curvature of the universe at different redshifts are obtained, with a statistically significant curvature of $\Omega_k=0.08\pm0.31$. This implies that, at the current observational level, it supports a flat universe.
Some argue that the reasons for the Hubble crisis and the curvature tension may be the failure of the standard cosmological model $\Lambda$CDM. Therefore, it is necessary to test the effectiveness of $\Lambda$CDM. Before directly testing the effectiveness of $\Lambda$CDM, this paper studies the invariance of the speed of light, indirectly testing general relativity, and then further tests $\Lambda$CDM. Specifically, an independent method based on high-redshift Hubble diagrams of multi-band quasars is studied to constrain the speed of light, which is also only related to $D_L(z)$ and $H(z)$. For the luminosity distance $D_L(z)$ provided by the multi-band quasar Hubble diagram and the $H(z)$ provided by cosmic chronometers, the values of the variable speed of light parameter $\eta\equiv c/c_0$ at different redshifts are obtained. The statistically significant restriction result is $\eta=1.19\pm0.07$, with no strong evidence deviating from the constant value $\eta=1$.
Finally, the effectiveness of the standard cosmological model $\Lambda$CDM is tested using the $Omh^2$ diagnostic method, which is only related to $H(z)$. To ensure the model independence of the test, only the Hubble parameter $H(z)$ obtained from cosmic chronometers is considered. The sample includes 33 measurements of $H(z)$, with the highest redshift reaching 2.0. The values of $Omh^2$ at different redshifts are obtained, with a weighted average statistically analyzed result of $Omh^2=0.1438\pm0.0045$, consistent with the constraint result of $0.1428\pm0.0011$ from Planck 2018. Furthermore, compared with the cosmological models $\omega$CDM and CPL, the $\Lambda$CDM model performs better in the $Omh^2$ diagnostic method.
In summary, this paper focuses on galaxy cluster strong gravitational lensing and multi-band quasars as the main cosmological novel probes, studying hot issues in cosmology such as the Hubble constant, universe curvature, invariance of the speed of light, and the effectiveness of the standard cosmological model, and although no evidence of new physics has been found at the current observational level, some innovative and interesting conclusions have been obtained. With the continuous development of future observations, new physical laws may be revealed.