Axial Bianchi IX and its Lema{\^i}tre-Hubble diagram

TL;DR

This paper calculates the Lemaître-Hubble diagram for axial Bianchi IX universes with dust, revealing that negative curvatures are excluded under minimal symmetry breaking, thus refining cosmological models.

Contribution

It introduces a minimal symmetry breaking criterion that restricts Bianchi IX models to positive curvature cases with dust, excluding negative curvature scenarios.

Findings

Negative curvatures are excluded by the minimal symmetry breaking.

Bianchi IX universes with dust have positive curvature under the proposed criterion.

The work connects symmetry breaking with curvature properties in cosmological models.

Abstract

We compute the Lema{\^i}tre-Hubble diagram for axial Bianchi IX universes with comoving dust. We motivate our choice by defining a {\it minimal} symmetry breaking of the cosmological principle. This criterium admits only two possibilities: the axial Bianchi I and IX universes. The latter have positive curvatures and reduce to the former in the zero curvature limit. Remarkably, negative curvatures are excluded by this minimal symmetry breaking in presence of comoving dust.