Large scale structure simulations of inhomogeneous LTB void models

TL;DR

This paper presents numerical simulations of large-scale structure evolution in an inhomogeneous LTB model, showing that non-linear density and velocity profiles follow exact Einstein solutions, challenging previous claims about the necessity of relativistic codes.

Contribution

The study demonstrates that Newtonian-like simulations can accurately reproduce non-linear LTB solutions, questioning the need for fully relativistic codes in modeling large-scale structures.

Findings

Density contrast at the void center grows to order one

Profiles follow exact non-linear LTB solutions

Growth of density contrast resembles open universe dynamics

Abstract

We perform numerical simulations of large scale structure evolution in an inhomogeneous Lemaitre-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-deSitter model. We observe how the (background) density contrast at the centre of the void grows to be of order one, and show that the density and velocity profiles follow the exact non-linear 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 non-linear 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 OmegaM(r) corresponding to the appropriate location within the void.