Spatially-Homogeneous Cosmologies

TL;DR

This paper establishes precise, algorithmic conditions for perfect fluid solutions to be spatially homogeneous cosmologies, also determining their Bianchi type when a symmetry group acts on spatial orbits.

Contribution

It provides intrinsic, deductive, explicit, and algorithmic criteria for identifying spatially-homogeneous cosmologies and determining their Bianchi classification.

Findings

Derived necessary and sufficient conditions for spatial homogeneity.

Introduced an IDEAL labeling scheme for these geometries.

Connected symmetry group actions to Bianchi types.

Abstract

The necessary and sufficient conditions for a perfect fluid solution to define a spatially-homogeneous cosmology are achieved. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these geometries. When a three-dimensional group acts on the three-dimensional space-like orbits, the Bianchi type of the model is also obtained.