Analytic Expression of the Genus in Weakly Non-Gaussian Field Induced by Gravity

The gravitational evolution of the genus of the density field in large-scale structure is analytically studied in a weakly nonlinear regime using second-order perturbation theory. Weakly nonlinear evolution produces asymmetry in the symmetric genus curve for Gaussian initial density field. The effect of smoothing the density field in perturbation theory on the genus curve is also evaluated and gives the dependence of the asymmetry of the genus curve on spectra of initial fluctuations.