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

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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.