Large-scale structure of the Universe. Analytic theory.

An analytical theory is developed of the nonlinear stage of the Jeans instability in a cold nondissipative gas in an expanding Universe. It is shown that the growth of this instability creates a giant dark-matter halo, of $200$ kpc size, around galaxies. This halo has a density singularity described by $\rho\propto r^{-\alpha}$, where $\alpha\asymp1,7$–$1,9$. A comparison is made of this analytic theory with the results of numerical simulations and a good agreement between them is demonstrated. Analytic dynamic solutions are used to develop a statistical method for calculation of the correlation functions of galaxies and galaxy clusters. The theory is compared with the available observational data. The physical consequences of the proposed theory are considered.