TWO-DIMENSIONAL SIMULATION OF THE GRAVITATIONAL SYSTEM DYNAMICS AND FORMATION OF THE LARGE-SCALE STRUCTURE OF THE UNIVERSE

The results of a numerical experiment are given that describe the non-linear stages of the development of perturbations in gravitating matter density in the expanding Universe. This process simulates the formation of the large-scale structure of the Universe from an initially almost homogeneous medium. In the one- and two-dimensional cases of this numerical experiment the evolution of the system from 4096 point masses that interact gravitationally only was studied with periodic boundary conditions (simulation of the infinite space). The initial conditions were chosen that resulted from the theory of the evolution of small perturbations in the expanding Universe. The results of numerical experiments are systematically compared with the approximate analytic theory. The results of the calculations show that in the case of collisionless particles, as well as in the gas-dynamic case, the cellular structure appeared at the non-linear stage (when δρ/ρ 1) in the case of the adiabatic perturbations. The greater part of the matter is in thin layers that separate vast regions of low density. In a Robertson-Walker universe (Ω = 1) the cellular structure exists for a finite time and then fragments into a few compact objects. In the open Universe (Ω > 1) the cellular structure also exists if the amplitude of initial perturbations is large enough. But the following disruption of the cellular structure is more difficult because of too rapid an expansion of the Universe. The large-scale structure is frozen. Formation of the cellular structure depends mainly on the choice of the spectrum of initial perturbations (short waves must be suppressed). © 1980 Royal Astronomical Society.