About Bianchi I with time varying constants

TL;DR

This paper explores various symmetry-based techniques to analyze a Bianchi I cosmological model with time-varying gravitational and cosmological constants, revealing different solution classes and their physical implications.

Contribution

It compares multiple symmetry methods for solving Bianchi I models with variable G and Lambda, highlighting their differences and resulting solutions.

Findings

Lie groups method yields only flat FRW solution with constant G and zero Lambda.

Self-similarity, matter collineations, and kinematical self-similarity produce solutions with decreasing G and Lambda ~ t^{-2}.

Scale factor exponents satisfy relaxed Kasner conditions, depending on the equation of state.

Abstract

In this paper we study how to attack through different techniques a perfect fluid Bianchi I model with variable G, and $\Lambda.$ These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC). and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution with G=const. and $\Lambda=0$. The SS, MC and KSS approaches bring us to obtain the following solution: G is a decreasing time function and $\Lambda\thickapprox t^{-2}$, with $\Lambda<0$, 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.