宇宙学中最具挑战性的问题之一是理解晚期宇宙加速膨胀背后的物理机制。现在已经有许多的观测被用于探测这种正加速度背后的机制，如高红移Ia型超新星(SNe Ia)，宇宙微波背景辐射(CMB)，星系团，重子声波振荡(BAO)等。这些工具基于一个基本假设，即光子总数在宇宙尺度上是守恒的。这是宇宙距离对偶(cosmic distance duality，CDD)关系〓=1成立的关键假设之一，这个关系只与光度距离D〓和角直径距离D〓以及此处的红移值有关。这个等式又被称为艾丁顿(Etherington relation)关系，是艾丁顿于1933年提出的。CDD关系是表征在尺度因子变化的时空中两种距离的关系，对于所有基于黎曼几何的宇宙学模型都有效，在探索晚期宇宙加速膨胀时经常用到。这个关系在观测宇宙学中起着重要作用，特别是在星系观测，CMB观测和引力透镜中起着至关重要的作用。此外，CDD关系的偏离可能使度规引力理论在解释宇宙的背景动力学时失败而导致新物理学的出现。如可变的基本物理常数，轴子光子混合(axion-photon mixing)等标准模型以外的物理宇宙学理论。因此有必要精确地检验CDD关系，目前的检验中，光度距离的来源通常是通过观测到的超新星样本。而超新星样本给出的光度距离通常是与超新星的光变曲线参数相关，人们采用了诸如ACDM这样的模型得出这些光变曲线参数。由于CDD关系的成立条件，我们可以在非加速膨胀的宇宙学模型R〓=ct宇宙模型下检测CDD关系是否成立。我们的检测中，同先前的许多工作一样，宇宙学模型隐含在SNe Ia的光度距离里面。本篇博士论文就是利用多种数据检测CDD关系在两种宇宙学模型下的有效性，以及比较模型优劣。在考虑有宇宙学不透明度的情况下，研究标准烛光的偏离通过CDD关系传导给其他的宇宙学参数对于限制宇宙学模型参数的影响。 第一章，我们简要的介绍了一下宇宙学的基本知识，特别是标准宇宙学模型以及宇宙学距离的概念。第二章我们介绍了一下R〓=ct宇宙学模型以及利用星系团角直径距离和超新星光变曲线数据来同时限制CDD关系，宇宙学参数和SNe Ia的光变曲线参数系数。我们发现在同时限制的情况下，作为自由参数的哈勃常数和作为干扰参数的绝对星等不再简并，此时CDD关系对于H₀的变化很敏感。在适当的H₀取值之下，CDD关系都在2σ置信水平上成立。在本次检测所用的数据中，通过两种标准信息准则判断，平坦的ACDM模型要优于R〓=ct模型。我们也给出了CDD关系的一种与宇宙学模型独立的检测方法。第三章，我们分析了宇宙不透明度对于标准烛光限制宇宙学模型参数造成的影响，我们分析了其中的一种不透明度来源，即康普顿散射消光，讨论了这种效应对今后的超新星，GRB巡天的影响。其结果表明，依文中所用的数据，宇宙几乎是透明的，不透明度的影响不足以否定暗能量，康普顿散射消光对宇宙不透明的贡献为5％左右。在今后的巡天中，如WFIRST将观测超过2700颗超新星，需要考虑这种影响，以免造成系统误差。而对于GRB的情况，由于高能GRB光子散射截面小，康普顿散射消光效应造成的误差相对于GRB自身距离模数的系统误差要小一个数量级。所以可以忽略不计。第四章我们使用强引力透镜数据结合H(z)，BAO的数据来限制宇宙学模型参数，主要考虑了平坦的和有曲率的ACDM模型，幂律宇宙模型，以及作为幂律模型的特殊情况的R〓=ct宇宙模型。我们发现平坦的ACDM模型要更受数据支持，通过加入更多的数据集，基本上排除掉了幂律宇宙学模型，但是并不能得出平坦的ACDM宇宙学模型更好的结论。第五章，是我们完成上述工作所做的一点总结以及作者对于这个研究方向的一些展望。 关键词：宇宙学距离，宇宙学模型，宇宙距离对偶关系

 Understanding the physical mechanisms behind the accelerated expansion of the late universe is one of the most challenging problems in modern cosmology. Many observational methods are used to explore the mechanism of this positive acceleration, for instance, high redshift type Ia supernova (SNe Ia), cosmic microwave background (CMB), clusters of galaxies, baryon acoustic oscillations (BAO) etc. These tools are based on a fundamental assumption that the number of photons is conserved on cosmological scales. This is one of the key assumptions of the validity of Cosmic Distance Duality (CDD) relation 〓 = 1. The relation is only relate to the luminosity distance D〓 , the angular diameter distance D〓 and their common redshift. The above equation is also known as the Etherington relation, which was proposed by Eddington in 1933. The CDD relation is a representation of the relationship between the two kind of distances in space-time with a variable scale factor, and it is validity for all cosmology models which are base on Riemannian geometry. This relation are often used to explore the accelerated expansion of the late universe. This distance relation plays an important role in the observation of cosmology. In particular, it plays a vital role in galaxy observations, CMB observations, and gravitational lenses. In addition, any violations in CDD relation may point to the failure of metric gravity theory to explain the background dynamics of the cosmic and the emergence of new physics, such as variable basic physical constants, non-standard models like axion - photon mixing. Therefore, it is necessary to test the CDD relation accurately. In the current test, the sources of the D〓 are usually acquired from SNe Ia sample. These D〓 are related to the light curve parameters of the supernovae samples which are derived by a specific cosmological model such as the ΛCDM model. Due to the catholic condition of CDD relation, we can detect whether the CDD relationship is still valid under the non-accelerated cosmological model, ie, R〓 = ct universe model. In our tests, as with many previous works, cosmological models are implicit in the D〓 of SNe Ia. In this doctoral thesis, we use a variety of data to detect the effectiveness of CDD relation in two cosmological models, and to compare the pros and cons of the models. In the case of cosmological opacity, the deviation of the standard candle is transmitted through the CDD relationship to affect the other cosmological parameters. We will analyse these effects. In the first chapter, we introduce the basic knowledge of cosmology briefly, especially the standard cosmological model and the cosmological distance. In the second chapter, we introduce the physical idea of the R〓 = ct cosmological model and the constrain of CDD relation with the samples of supernova light curve data and the D〓 of the galaxy cluster. We find that in the case of simultaneous constraints, the Hubble constant as a free parameter and the absolute magnitude as a nuisance parameter are no longer degenerate, and the CDD relationship is sensitive to H₀. With an appropriate H₀, the CDD relationship is valid at the 2σ confidence level. Base on these samples, the flat ΛCDM model is better than the R〓 = ct model by two standard information criteria. A model independent method to test CDD relation is also given in this dissertation. In Chapter 3, we analyse the effects of cosmic opacity when using standard candle to constrain the parameters of cosmological model. We analyzed one of the sources of opacity, namely, Compton scattering extinction, and the effect of future SNe, GRB surveys. The results show that the universe is almost transparent according to the data. The effect of opacity is not enough to rule out dark energy. The contribution of Compton scattering extinction to the opacity of the universe is about 5%. In the future survey, WFIRST will observe more than 2,700 supernovae thus this effect is needed to be considered to avoid system errors. In the case of GRB, since the scattering cross section of high-energy GRB photon is small, the error caused by Compton scattering extinction is one order of magnitude smaller than the systematic error of distance modulus, so it can be ignored. In Chapter 4, we use strong gravitational lens data combined with H(z), BAO sample to constrain the parameters of cosmological models. The ΛCDM model with curve parameter and the power law cosmology model are considered. The result shows that the ΛCDM models are more better than the others. With more and more data, the power law and the R〓 = ct model can be eliminated. But, the two ΛCDM model, we can not eliminate either of one with these data samples. In Chapter 5, we summerize our results and give a brief look into the future. keywords: cosmology distance, cosmology model, cosmic distance duality