The abundance of voids and the excursion set formalism

Understand

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.