Internal symmetry in Bianchi type-I cosmologies

TL;DR

This paper explores the internal symmetry group in Bianchi type-I cosmologies, revealing coordinate systems where two scale factors are equal, and provides exact solutions for anisotropic fluids, enhancing understanding of anisotropic universe models.

Contribution

It introduces a method to find coordinate systems with equal scale factors in Bianchi type-I models and derives exact solutions for specific anisotropic fluids.

Findings

Existence of coordinate systems with two equal scale factors.

General solutions for anisotropic models with constant baryotropic index.

Exact solutions for anisotropic stiff fluids.

Abstract

Using the one-parameter internal symmetry group in the Bianchi type-I spacetime for cosmological models with a perfect fluid, we show that a system of coordinates exists in the associated internal space where two scale factors become equal. We find the general solution for an anisotropic model containing a perfect fluid with constant baryotropic index and investigate the asymptotic regimes. We obtain exact solutions for a set of anisotropic fluids which includes an anisotropic stiff fluid.