Weakly Nonlinear Evolution of Topology of Large-scale Structure

TL;DR

This paper derives an analytical model for the weakly nonlinear evolution of the topology of large-scale cosmic structures, comparing it with simulations to validate its accuracy.

Contribution

It provides a new analytical expression for the genus statistic in the weakly nonlinear regime, incorporating smoothing effects and validated against N-body simulations.

Findings

Analytic expression for genus matches simulations well

Smoothing effects are quantitatively evaluated in perturbation theory

Weakly nonlinear evolution impacts topology statistics significantly

Abstract

The gravitational evolution of the genus and other statistics of isodensity contours of the density field is derived analytically in a weakly nonlinear regime using second-order perturbation theory. The effect of final smoothing in perturbation theory on the statistics of isodensity contours is also evaluated. The resulting analytic expression for the genus is compared with $N$-body numerical simulations and exhibits a good agreement.