Bianchi I with variable $G$ and $\Lambda$. Self-Similar approach

TL;DR

This paper investigates a Bianchi I cosmological model with variable gravitational and cosmological constants under self-similarity, revealing their decreasing nature over time and relaxing Kasner conditions, with links to the Weyl tensor.

Contribution

It introduces a self-similar approach to Bianchi I models with variable G and Lambda, relaxing Kasner conditions and analyzing their relation to the Weyl tensor.

Findings

G and Lambda decrease over time

Exponents satisfy sum conditions relaxing Kasner constraints

Connection established between G behavior and Weyl tensor

Abstract

In this paper we study how to attack under the self-similarity hypothesis a perfect fluid Bianchi I model with variable $G,$and $\Lambda,$ but under the condition $\operatorname{div}T\neq0.$ We arrive to the conclusion that: $G$ and $\Lambda$ are decreasing time functions (the sing of $\Lambda$ depends on the equation of state), while the exponents of the scale factor must satisfy the conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$ $\forall\omega\in(-1,1) ,$ relaxing in this way the Kasner conditions. We also show the connection between the behavior of $G$ and the Weyl tensor.