Bianchi {VI}$_{0}$ in Scalar and Scalar-Tensor Cosmologies

TL;DR

This paper investigates Bianchi VI$_0$ cosmological models with variable gravitational and cosmological constants, exploring perfect fluid, scalar field, and scalar-tensor scenarios, and analyzing their behavior and isotropization.

Contribution

It introduces new solutions for Bianchi VI$_0$ models with variable $G$ and $\\Lambda$, including a novel perfect fluid solution and multiple scalar-tensor solutions.

Findings

$G$ and $\\Lambda$ are interrelated, with $G$'s behavior affecting $\\Lambda$'s sign and magnitude.

New exact solutions are found for different $G$ behaviors in scalar-tensor models.

Solutions exhibit varying degrees of isotropization based on curvature invariants.

Abstract

We study several cosmological models with Bianchi \textrm{VI}$_{0}$ symmetries under the self-similar approach. In order to study how the \textquotedblleft constants\textquotedblright\ $G$ and $\Lambda$ may vary, we propose three scenarios where such constants are considered as time functions. The first model is a perfect fluid. We find that the behavior 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 $\Lambda$ is negative. For this model we have found a new solution. The second model is a scalar field, where in a phenomenological way, we consider a modification of the Klein-Gordon equation in order to take into account the variation of $G$. Our third scenario is a scalar-tensor model. We find three solutions for this models where $G$ is growing, constant or decreasing and $\Lambda$ is a positive decreasing function or vanishes. We put special emphasis on calculating the curvature invariants in order to see if the solutions isotropize.