The abundance of voids and the excursion set formalism
  We present measurements of the number density of voids in the dark matter
distribution from a series of N-body simulations of a \Lambda CDM cosmology. We
define voids as spherical regions of \rho_v = 0.2\rho_m around density minima
in order to relate our results to the predicted abundances using the excursion
set formalism. Using a linear underdensity of \delta_v = -2.7, from a spherical
evolution model, we find that a volume conserving model, which does not
conserve number density in the mapping from the linear to nonlinear regime,
matches the measured abundance to within 16% for a range of void radii 1<
r(Mpc/h)<15. This model fixes the volume fraction of the universe which is in
voids and assumes that voids of a similar size merge as they expand by a factor
of 1.7 to achieve a nonlinear density of \rho_v = 0.2\rho_m today. We find that
the model of Sheth & van de Weygaert (2004) for the number density of voids
greatly overpredicts the abundances over the same range of scales. We find that
the volume conserving model works well at matching the number density of voids
measured from the simulations at higher redshifts, z=0.5 and 1, as well as
correctly predicting the abundances to within 25% in a simulation of a matter
dominated \Omega_m = 1 universe. We examine the abundance of voids in the halo
distribution and find fewer small, r<10 Mpc/h, voids and many more large, r>10
Mpc/h, voids compared to the dark matter. These results indicate that voids
identified in the halo or galaxy distribution are related to the underlying
void distribution in the dark matter in a complicated way which merits further
study if voids are to be used as a precision probe of cosmology.
