Bianchi II with time varying constants. Self-similar approach

TL;DR

This paper investigates Bianchi II cosmological models with time-varying constants G, Lambda, and c, using a self-similar approach, revealing that G and c increase over time while Lambda decreases, consistent with current observations.

Contribution

It introduces a more general self-similar solution for Bianchi II models with variable G, Lambda, and c, extending classical solutions to broader equations of state.

Findings

G must be a growing function over time.

Lambda is a positive decreasing function.

c must be a growing function if Lambda decreases.

Abstract

We study a perfect fluid Bianchi II models with time varying constants under the self-similarity approach. In the first of the studied model, we consider that only vary $G$ and $\Lambda.$ The obtained solution is more general that the obtained one for the classical solution since it is valid for an equation of state $\omega\in(-1,\infty) $ while in the classical solution $\omega\in(-1/3,1) .$ Taking into account the current observations, we conclude that $G$ must be a growing time function while $\Lambda$ is a positive decreasing function. In the second of the studied models we consider a variable speed of light (VSL). We obtain a similar solution as in the first model arriving to the conclusions that $c$ must be a growing time function if $\Lambda$ is a positive decreasing function.