Cosmological models with flat spatial geometry

TL;DR

This paper investigates a class of irrotational dust cosmological models with flat hypersurfaces, relaxing the Cosmological Principle, and uses covariant and tetrad methods to classify and analyze their properties.

Contribution

It provides a complete classification of flat hypersurface irrotational dust models and explores their physical and geometric properties, extending cosmological model understanding.

Findings

Classified all models with flat hypersurfaces and irrotational dust

Analyzed geometric and physical properties of these models

Discussed implications for cosmological principles

Abstract

The imposition of symmetries or special geometric properties on submanifolds is less restrictive than to impose them in the full space-time. Starting from this idea, in this paper we study irrotational dust cosmological models in which the geometry of the hypersurfaces generated by the fluid velocity is flat, which supposes a relaxation of the restrictions imposed by the Cosmological Principle. The method of study combines covariant and tetrad methods that exploits the geometrical and physical properties of these models. This procedure will allow us to determine all the space-times within this class as well as to study their properties. Some important consequences and applications of this study are also discussed.