Bianchi VI_0&III models. Self-similar approach

TL;DR

This paper explores self-similar solutions in Bianchi VI_0&III cosmological models, including perfect fluids, vacuum, and string models, revealing new solutions and the relationship between varying constants G and Λ.

Contribution

It introduces new self-similar solutions for Bianchi VI_0&III models, including models with time-varying G and Λ, and analyzes the absence of solutions for string models with varying constants.

Findings

New solutions for classical perfect fluid and vacuum models.

G and Λ are interrelated, with G's behavior influencing Λ's sign and magnitude.

No self-similar solution exists for string models with time-varying constants.

Abstract

We study several cosmological models with Bianchi VI_0&III symmetries under the self-similar approach. We find new solutions for the "classical" perfect fluid model as well as for the vacuum model although they are really restrictive for the equation of state. We also study a perfect fluid model with time-varying constants, $G$ and $\Lambda.$ As in other models studied we find that the behaviour of $G$ and $\Lambda$ are related. If $G$ behaves as a growing time function then $\Lambda$ is a positive decreasing time function but if $G$ is decreasing then $\Lambda_{0}$ is negative. We end by studying a massive cosmic string model, putting special emphasis on calculating the numerical values of the equations of state. We show that there is no SS solution for a string model with time-varying constants.