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 cold dark matter cosmology. We define voids as spherical regions of v = 0.2 m around density minima in order to relate our results to the predicted abundances using the excursion set formalism. Using a linear underdensity of 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 non-linear regime, matches the measured abundance to within 16 per cent for a range of void radii 1 10 h -1 Mpc, 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.