ONE-DIMENSIONAL SIMULATIONS OF INHOMOGENEITY GROWTH IN PRESSURELESS GRAVITATING MATTER

Abstract

We study a model of the inhomogene­ity growth in the Universe filled with a pressureless matter. The standard hydrodynamical equations for the cosmological perturbations in the comoving frame are treated taking into account all nonlinear terms. We consider perturbations of the uniform isotropic cosmological background but with plane periodic initial conditions for the perturbations. The problem is reduced to ordinary differential equations for an in­finite chain of Fourier coefficients for hydrodynamical variables. We perform a numerical integration of these equations (with proper truncation) for an ensemble of random initial conditions. The power spectrum of the density contrast in obtained by means of an averaging procedure.