The Analysis of the Gravitational Growth of the Matter, Thermal Evolution and the CMB anisotropies, which are related to the Large-Scale Structures Formations.

分析了与大尺度结构和星系形成密切相关的宇宙密度涨落的引力增长的非线性动力学和星系团的模式。进一步分析了暗晕的合并历史和星系动力学，这是星系形成和演化的重要过程。通过这些分析，我得到了以下结果：1)用伪谱法得到了密度涨落非线性增长中的非线性傅里叶模式耦合规律。2)证明了密度涨落功率谱的功率指数仅由二维和三维系统中按照突变理论分类的奇点类型决定。进一步通过分析BBGKY方程的标度不变解，得到了两点相关函数的幂指数与强非线性状态下其他量的关系。3)得到了一维自引力多体系统弛豫到准平衡态的时间尺度。进一步证明了系统存在许多准平衡状态，并且系统在这些状态之间徘徊。发现过渡时间尺度的分布服从幂律。我们认为这是由于对应于准平衡态的部分空间在整个相空间中以分形形式分布的结果。4)我们澄清了通常用于估计暗晕质量函数的Press-Schechter形式的局限性。进一步表明，在分析暗晕合并历史时，考虑空间相关的影响是非常重要的。5)我们通过考虑星系的整体流动，估计了在局部宇宙中观测到的哈勃常数与全球哈勃常数之间的差异。

I analyzed the nonlinear dynamics of the gravitational growth of cosmological density fluctuations and the pattern of clustering which are much related to the large-scale structure and galaxy formations. Furthermore I analyzed the merging history of dark haloes and galactic dynamics which are very important processes in the formations and evolutions of the galaxies. I got the following results by these analysis ;1) I got the law of nonlinear Fourier-mode coupling in the nonlinear growth of density fluctuations by the pseudo-spectral method.2) I showed that the power index of the power spectrum of density fluctuations is determined only by the type of singularity which is classified in accord with the catastrophe theory in both two-dimensional and three-dimensional systems. Furthermore we found the relation between the power index of the two-point correlation function and other quantities in the strongly nonlinear regime by the analysis of scale-invariant solutions of the BBGKY equation.3) We found the time scale of the relaxation to the quasi-equilibrium state in the one-dimensional self-gravitating many-body systems. Furthermore we showed that there are many quasi-equilibrium states and the system wanders between the states. The distribution of time scale of transition is found to obey the power law. We believe that this is resulted from the fact that partial space which corresponds to a quasi-equilibrium state distributes in the fractal form in the whole phase space.4) We clarified the limitations of the Press-Schechter formalism which is often used for estimate of the mass functions of dark haloes. Furthermore we showed that it is very important to consider the effect of spatial correlation in analyzing the merging history of dark haloes.5) We estimated the difference between the Hubble constant observed in the local universe and the global Hubble constant by taking into account the bulk flows of galaxies.