Dynamical Equilibrium States of a Class of Irrotational Non-Orthogonally Transitive $G_2$ Cosmologies I: The Conjecture of Chaotic Cosmological Inhomogeneity

Abstract

The Einstein field equations for a class of irrotational non-orthogonally transitive $G_2$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a one-parameter, five-dimensional, ordinary differential equation. The corresponding cosmological models both evolve and have one-dimension of inhomogeneity. The major mathematical features of this ordinary differential equation are derived, and a cosmological interpretation is given. The relationship to the exceptional Bianchi models is explained and exploited to provide a conjecture about future generalizations.

Only change is added reference to companion paper arxiv.org:2103.16428

References in corpus (1)

• Cosmological models from a geometric point of view