On the intrinsically flat cosmological models in a lattice

TL;DR

This paper explores intrinsically flat cosmological models with periodic inhomogeneous matter distributions, establishing their mathematical properties and presenting exact solutions that resemble realistic universe features.

Contribution

It introduces a geometric framework for space-flat spacetimes with periodic matter patterns and proves key theorems on their mathematical properties and solutions.

Findings

Existence and uniqueness of Einstein's equations with periodic boundary conditions.

A class of exact solutions with early homogeneity and late-time inhomogeneities.

Models exhibit peaks and voids similar to cosmic structures.

Abstract

In this manuscript we investigate the intrinsically flat (space-flat) spacetimes as viable cosmological models. We show that they have a natural geometric structure which is suitable to describe inhomogeneous matter distributions forming a periodic pattern throughout the space. We prove theorems for their local representation and for existence and uniqueness of the Einstein's equations with these periodic boundary conditions. We also find an interesting class of exact solutions, which illustrates the applicability of such spacetimes in cosmology, with an early time behavior close to homogeneity and isotropy and a late time aspect with peaks and voids in the matter distribution.