Nonlinear Evolution of Genus in Primordial Random-Gaussian Density Field

The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space distortion on the genus curve. Detailed comparison between the theoretical prediction in weakly nonlinear theory and the appropriate simulation results shows that the analytic formula describes the behavior of genus in weakly nonlinear regime fairly accurately. We also find that the redshift-space distortion on genus statistics is small in linear and weakly nonlinear regimes. We conclude that if weakly nonlinear theory and direct numerical simulations are combined, the normalized genus curve $G(\nu )\mathrm{/}G(0)$ is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe.