A Hierarchy of Voids

Abstract

We present a model for the distribution of void sizes and its evolution within the context of hierarchical scenarios of gravitational structure formation. For a proper description of the hierarchical buildup of the system of voids in the matter distribution, not only the "void-in-void" problem should be taken into account, but also that of the "void-in-cloud" issue. Within the context of the excursion set formulation of an evolving void hierarchy is one involving a "two-barrier" excursion problem, unlike the "one-barrier" problem for the dark halo evolution. This leads to voids having a peaked size distribution at any cosmic epoch, centered on a characteristic void size that evolves self-similarly in time, this in distinct contrast to the distribution of virialized halo masses which do not have a small-scale cut-off.