Self-similar Bianchi models: I. Class A models

TL;DR

This paper analyzes class A Bianchi cosmological models with self-similarity, providing general solutions and showing the non-existence of certain models, thereby advancing understanding of anisotropic universe models.

Contribution

It derives the general form of self-similar solutions for class A Bianchi models and establishes the non-existence of specific self-similar Bianchi VII$_0$ and VI$_0$ models.

Findings

General solutions for Bianchi II self-similar models.

Proof of non-existence for Bianchi VII$_0$ and VI$_0$ self-similar models.

Explicit form of the homothetic vector field in these models.

Abstract

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.