Invariant Bianchi type I models in $f\left(R,T\right)$ Gravity

TL;DR

This paper finds invariant solutions for Bianchi type I cosmological models in $f(R,T)$ gravity using Lie symmetry analysis, revealing models with and without big bang singularities and exploring their physical features.

Contribution

It introduces new invariant solutions of Bianchi type I models in $f(R,T)$ gravity using Lie symmetry analysis, including singular and non-singular universe models.

Findings

One model begins with a big bang singularity.

Another model does not favor a big bang singularity.

Physically valid features are identified in the solutions.

Abstract

In this paper, we search the existence of invariant solutions of Bianchi type I space-time in the context of $f\left(R,T\right)$ gravity. The exact solution of the Einstein's field equations are derived by using Lie point symmetry analysis method that yield two models of invariant universe for symmetries $X^{(1)}$ and $X^{(3)}$. The model with symmetries $X^{(1)}$ begins with big bang singularity while the model with symmetries $X^{(3)}$ does not favour the big bang singularity. Under this specification, we find out at set of singular and non singular solution of Bianchi type I model which present several other physically valid features within the framework of $f\left(R,T\right)$.