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

摘要

We analyse the dynamics of trapped matter shells in spherically symmetricinhomogeneous \Lambda-CDM models. The investigation uses a GeneralisedLema\^itre-Tolman-Bondi description with initial conditions subject to theconstraints of having spatially asymptotic cosmological expansion, initialHubble-type flow and a regular initial density distribution. We discuss theeffects of shell crossing and use a qualitative description of the localtrapped matter shells to explore global properties of the models. Once shellcrossing occurs, we find a splitting of the global shells separating expansionfrom collapse into, at most, two global shells: an inner and an outer limittrapped matter shell. In the case of expanding models, the outer limit trappedmatter shell necessarily exists. We also study the role of shear in thisprocess, compare our analysis with the Newtonian framework and give concreteexamples using density profile models of structure formation in cosmology.