Merging Tree Algorithm of Growing Voids in Self Similar and CDM Models
  Observational studies show that voids are prominent features of the large
scale structure of the present day Universe. Even though their emerging from
the primordial density perturbations and evolutionary patterns differ from dark
matter halos, N-body simulations and theoretical models have shown that voids
also merge together to form large void structures. In this study, following
Sheth & van de Weygaert (2004), we formulate an analytical approximate
description of the hierarchical void evolution of growing voids by adopting the
halo merging algorithm given by Lacey & Cole (1993) in the Einstein de Sitter
(EdS) Universe. To do this, we take into account the general volume
distribution of voids which consists of two main void processes: merging and
collapsing. We show that the volume distribution function can be reduced to a
simple form, by neglecting the collapsing void contribution since the collapse
process is negligible for large size voids. Therefore, the void volume fraction
has a contribution only from growing voids. This algorithm becomes the analogue
of the halo merging algorithm. Based on this growing void distribution, we
obtain the void merging algorithm in which we define and formulate void merging
and absorption rates, as well as void size and redshift survival probabilities
and also failure rates in terms of the self similar and currently favored dark
energy dominated cold dark matter models in the EdS Universe.
