Statistics and geometry of cosmic voids

TL;DR

This paper introduces new statistical methods to analyze cosmic voids, linking their size distributions to fractal geometries of the universe, and supports a non-lacunar multifractal model consistent with observations.

Contribution

It presents a novel framework connecting void size distributions with fractal geometries and proposes models of the cosmic web supported by current data.

Findings

Void size distributions are classified into Poisson-like, lognormal-like, and Pareto-like types.

Pareto distributions relate to lacunar fractals with box-counting dimension less than three.

Current galaxy surveys support a non-lacunar multifractal model of the universe.

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.