Large scale structure simulations of inhomogeneous Lemaître-Tolman-Bondi void models

Abstract

We perform numerical simulations of large scale structure evolution in an inhomogeneous Lema\^{\i}tre-Tolman-Bondi (LTB) model of the Universe. We follow the gravitational collapse of a large underdense region (a void) in an otherwise flat matter-dominated Einstein--de Sitter model. We observe how the (background) density contrast at the center of the void grows to be of order one, and show that the density and velocity profiles follow the exact nonlinear LTB solution to the full Einstein equations for all but the most extreme voids. This result seems to contradict previous claims that fully relativistic codes are needed to properly handle the nonlinear evolution of large scale structures, and that local Newtonian dynamics with an explicit expansion term is not adequate. We also find that the (local) matter density contrast grows with the scale factor in a way analogous to that of an open universe with a value of the matter density ${\ensuremath{\Omega}}_{M}(r)$ corresponding to the appropriate location within the void.