A hierarchy of voids

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, in distinct contrast to the distribution of virialized halo masses in not having a small-scale cut-off.