F(R,..) theories from the point of view of the Hamiltonian approach: non-vacuum Anisotropic Bianchi type I cosmological model

In this work, we will explore the effects of F® theories in the classical scheme using the anisotropic Bianchi Type I cosmological model with standard matter employing a barotropic fluid with equation of state $P=\gamma \rho$. In this work we present the classical solutions in two gauge, N=1 and $N=6ABCD=6{\eta }^{3}D$ obtaining some results that are usually used as ansatz to solve the Einstein field equation. For completeness, we present the solutions in vacuum as well.