Statistics and geometry of cosmic voids

Abstract

We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distribution. Scaling voids with Pareto distribution appear in fractal distributions with box-counting dimension smaller than three (its maximum value), whereas the lognormal void distribution corresponds to multifractals with box-counting dimension equal to three. Moreover, voids of the former type persist in the continuum limit, namely, as the number density of observable objects grows, giving rise to lacunar fractals, whereas voids of the latter type disappear in the continuum limit, giving rise to non-lacunar (multi)fractals. We propose both lacunar and non-lacunar multifractal models of the cosmic web structure of the Universe. A non-lacunar multifractal model is supported by current galaxy surveys as well as cosmological $N$-body simulations. This model suggests, in particular, that small dark matter halos and, arguably, faint galaxies are present in cosmic voids.

39 pages, 8 EPS figures, supersedes arXiv:0802.0387

References in corpus (8)

• The Aspen--Amsterdam Void Finder Comparison Project
• Minivoids in the Local Volume
• Halos and voids in a multifractal model of cosmic structure
• Voids in the SDSS Galaxy Survey
• Properties of Voids in the 2dFGRS Galaxy Survey
• Fractal distributions of dark matter and gas in the MareNostrum Universe
• Generalized statistical models of voids and hierarchical structure in cosmology
• Cut-out sets, fractal voids and cosmic structure

Cited by in corpus (10)

• Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor
• Dead calm areas in the very quiet Sun
• The Fractal Geometry of the Cosmic Web and its Formation
• Fractal distributions of dark matter and gas in the MareNostrum Universe
• Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey
• On de-Sitter Geometry in Cosmic Void Statistics
• Smooth halos in the cosmic web
• Scale Symmetry in the Universe
• The Impact of $f(\mathcal{G},T)$ Gravity on the Evolution of Cavity in the Cluster of Stars
• Analysis of Cosmological Generalized Reduced Void Probability Functions Constrained by Observations and Numerical Simulations