宇宙空洞的几何学和尺度
Geometry and scaling of cosmic voids
摘要：
宇宙空洞在星系的分布中被观察到，在某种程度上，在暗物质的分布中也被观察到。如果这些分布具有分形几何，则它必须反映在空隙的几何形状中;特别是，我们期望空隙的尺寸缩放。然而，这种缩放在星系调查中还没有得到很好的证明。目的：我们的目标是了解宇宙空洞的几何形状与物质的分形结构的关系。我们打算区分单分形空洞从多重分形空洞，关于他们的标度特性。我们计划分析空隙的质量浓度分布（晕）的多重分形和它们的关系，星系空隙。方法：根据空泡概率函数和关联函数对点分布进行统计分析。我们假设空洞是球形的，并设计了一个简单的球形空洞探测器。对于连续质量分布，我们采用分形几何的方法。我们证实了分析预测与数值模拟。平滑质量分布适用于偏移集方法。结果：空穴是非常非线性和非微扰的结构。空隙反映了物质分布的分形几何形状，但并不总是直接的：空隙的标度尺寸意味着分形几何形状，但分形空隙可能具有复杂的几何形状，并且可能没有标度尺寸。真正的多重分形空洞就是这种类型。一个自然的多重分形偏置模型意味着星系分布中的空洞继承了同样复杂的几何形状。结论：目前的星系调查以及宇宙学N体模拟表明，宇宙空洞是适当的多重分形空洞。这意味着在星系的空隙中存在着，或者至少是小的暗物质晕。
英文摘要：
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objective is to understand the geometry of cosmic voids in relation to a fractal structure of matter. We intend to distinguish monofractal voids from multifractal voids, regarding their scaling properties. We plan to analyse voids in the distributions of mass concentrations (halos) in a multifractal and their relation to galaxy voids. METHODS: We make a statistical analysis of point distributions based on the void probability function and correlation functions. We assume that voids are spherical and devise a simple spherical void finder. For continuous mass distributions, we employ the methods of fractal geometry. We confirm the analytical predictions with numerical simulations. Smoothed mass distributions are suitable for the method of excursion sets. RESULTS: Voids are very nonlinear and non-perturbative structures. Voids reflect the fractal geometry of the matter distribution but not always directly: scaling sizes of voids imply fractal geometry, but fractal voids may have a complicated geometry and may not have scaling sizes. Proper multifractal voids are of this type. A natural multifractal biasing model implies that the voids in the galaxy distribution inherit the same complicated geometry. CONCLUSIONS: Current galaxy surveys as well as cosmological N-body simulations indicate that cosmic voids are proper multifractal voids. This implies the presence in the voids of galaxies or, at least, small dark matter halos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
