Modeling Gravitational Clustering without Computing Gravitational Force

Abstract

The large-scale structure in the Universe is believed to arise out of small random density perturbations generated in the very early Universe, that are amplified by gravity. Large and usually intricate N-body simulations are typically employed to model the complex nonlinear dynamics in a self gravitating medium. We suggest a very simple model which predicts, on large scales, the correct density and velocity distributions. The model does not involve an explicit computation of the gravitational force. It is based on a simple transformation of the variables and local conservation laws of mass and {\it generalized} linear momentum. The model demonstrates that the overall appearance of large-scale structure in the Universe is explicitly determined by the initial velocity field and it reveals the most significant large-scale effects of gravity on the formation of structure.