Stability of non-homegeneous models and fine tuning of initial state

TL;DR

This paper uses phase space analysis to examine the stability of inhomogeneous cosmological models, finding that such models generally exhibit instabilities that challenge their physical viability.

Contribution

It applies phase space analysis to Lemaître-Tolman models and assesses their stability, providing insights into the viability of non-homogeneous cosmologies.

Findings

Homogeneous models with cosmological constant can be stable

Inhomogeneous models show instabilities in phase space

Non-homogeneous models are unlikely to be physically viable

Abstract

We apply phase space analysis to inhomogeneous cosmological model given by Lema\^itre-Tolman model. We describe some general conditions required to interpret the model stable enough and, in the present paper, apply them to two special cases: dust filled homogeneous model with and without cosmological constant. We find that such stability explaining all present astrophysical observations can not be achieved due to instabilities in phase space. This hints that non-homogeneous models are not likely to be physically viable, although any conclusive analysis requires more realistic modeling of non-homogeneous universe.