The role of shell crossing on the existence and stability of trapped matter shells in spherical inhomogeneous \Lambda-CDM models

TL;DR

This paper investigates how shell crossing affects the existence and stability of trapped matter shells in spherical inhomogeneous DM models, revealing that shell crossing leads to a splitting of global shells and examining the role of shear.

Contribution

It provides a detailed analysis of shell crossing effects on trapped matter shells in DM models using a generalized Lema4tre-Tolman-Bondi framework, including concrete cosmological examples.

Findings

Shell crossing causes a splitting of global shells into inner and outer trapped matter shells.

An outer limit trapped matter shell always exists in expanding models.

Shear influences the dynamics and stability of trapped matter shells.

Abstract

We analyse the dynamics of trapped matter shells in spherically symmetric inhomogeneous \Lambda-CDM models. The investigation uses a Generalised Lema\^itre-Tolman-Bondi description with initial conditions subject to the constraints of having spatially asymptotic cosmological expansion, initial Hubble-type flow and a regular initial density distribution. We discuss the effects of shell crossing and use a qualitative description of the local trapped matter shells to explore global properties of the models. Once shell crossing occurs, we find a splitting of the global shells separating expansion from collapse into, at most, two global shells: an inner and an outer limit trapped matter shell. In the case of expanding models, the outer limit trapped matter shell necessarily exists. We also study the role of shear in this process, compare our analysis with the Newtonian framework and give concrete examples using density profile models of structure formation in cosmology.