标题： 早期随机高斯密度场中拓扑的非线性演化 显示英文标题

标题： Nonlinear Evolution of Genus in Primordial Random-Gaussian Density Field

摘要： 我们利用几个宇宙学模型的大规模 $N$ 体模拟研究了 genus 统计。 我们考虑了非线性引力演化的影响，在完全非线性区域平滑粒子数据，以及红移空间失真对 genus 曲线的影响。 弱非线性理论中的理论预测与适当的模拟结果的详细比较表明，解析公式相当准确地描述了弱非线性区域中 genus 的行为。 我们还发现，genus 统计的红移空间失真在线性和弱非线性区域都很小。 我们得出结论，如果结合弱非线性理论和直接数值模拟，归一化的 genus 曲线 $G(\nu)/G(0)$ 是一个强有力的工具，可以直接检验宇宙大尺度结构随机-高斯起源范式的正确性。 显示英文摘要

摘要： 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 $G(\nu)/G(0)$ is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe.