Nonlinear Evolution of Topology of Large Scale Structure
Takahiko Matsubara · 1996
As a statistical measure of large-scale structure of the universe, the genus number is presented in analytic form for realistic non-Gaussian distributions, i.e., weakly non-Gaussian, lognormal and chi-square distributions. These formulae are compared with the results of N - body simulation. It is shown that the weakly non-Gaussian formula describes the behavior of genus in weakly nonlinear regime fairly accurately and that the lognormal formula fits the simulation data the best in mildly nonlinear regime. We conclude that if analytic formulae and direct numerical simulations are combined, the normalized genus curve G()=G(0) is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe. 1. Introduction To characterize the pattern of the structures in the universe, the topological analysis of the galaxy distribution provides a useful and intuitively clear way. Gott, Melott & Dickinson (1986) proposed to use the Euler charac...