Geometric and physical properties of closed ever expanding dust models

TL;DR

This paper investigates closed, ever-expanding dust cosmological models with positive spatial curvature, showing that a positive cosmological constant can eliminate unphysical features and supporting its inclusion in realistic models.

Contribution

It demonstrates that positive cosmological constant removes unphysical distributional sources in closed LTB models, favoring a nonzero Lambda in cosmology.

Findings

Unphysical features appear in LTB models with zero Lambda at large times.

A positive Lambda eliminates these unphysical behaviors.

Results support including a positive cosmological constant in cosmological models.

Abstract

Current observations suggest that our Universe is not incompatible with a small positive spatial curvature that can be associated with rest frames having a "closed" standard topology. We examine a toy model generalisation of the $\Lambda$CDM model in the form of ever expanding Lema\^{i}tre-Tolman-Bondi (LTB) models with positive spatial curvature. It is well known that such models with $\Lambda=0$ exhibit a thin layer distribution at the turning values of the area distance that must be studied through the Israel-Lanczos formalism. We find that this distributional source exhibits an unphysical behaviour for large cosmic times and its presence can be detected observationally. However, these unphysical features can always be avoided by assuming $\Lambda >0$. While these LTB models are very simplified, we believe that these results provide a simple argument favouring the assumption of a nonzero positive cosmological constant in cosmological models.