Halo abundances and shear in void models

We study the non-linear gravitational collapse of dark matter into halos through numerical N-body simulations of Lemaître–Tolman–Bondi void models. We extend the halo mass function formalism to these models in a consistent way. This extension not only compares well with the simulated data at all times and radii, but it also gives interesting clues about the impact of the background shear on the growth of perturbations. Our results give hints about the possibility of constraining the background shear via cluster number counts, which could then give rise to strong constraints on general inhomogeneous models, of any scale.