Nonlinear dynamics of the large-scale structure in the universe

Abstract

This paper briefly reviews the nonlinear gravitational dynamics in an expanding universe. The gravitational instability is believed to play a key role in the formation of the large-scale structure of the universe, amplifying primordial small-amplitude random density fluctuations of Gaussian type and then, at the nonlinear stage, transforming them into thin dense pancakes, filaments, and compact clumps of matter. Although there are evidences that the distribution of galaxies and the distribution of the underlying mass density are not quite the same, it is widely accepted that they become similar when smoothed with a window of a sufficiently large size. At present the formation of galaxies themselves is very poorly understood and is not discussed here. We discuss scales in the range roughly from 1 Mpc to 100 Mpc (≈ 3 × 10 24 - 3 × 10 26 cm). The lower limit is at least 50 times greater than the size of the luminous part of a large galaxy, and the upper limit is at least 30 times smaller than the size of the observed universe. The problem of the formation of the large-scale structure is one of the key problems in modern cosmology and has too many aspects to mention in a short paper. Instead I review only the nonlinear evolution of density inhomogeneities on scales in question, which occured relatively recently. The paper discusses mainly analytical and semianalytical methods used in examining the nonlinear gravitational dynamics of the large-scale structure, though many hints were found in N-body simulations which have played a very important role in confronting theoretical models with observations.