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