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

TL;DR

This paper investigates F(R) gravity theories within the Hamiltonian framework applied to an anisotropic Bianchi Type I cosmological model, analyzing classical solutions with matter and vacuum cases.

Contribution

It provides classical solutions for F(R) theories in Bianchi Type I models using Hamiltonian methods, including non-vacuum and vacuum scenarios, in different gauges.

Findings

Derived classical solutions in two gauge choices.

Presented solutions with matter and vacuum cases.

Used solutions as ansatz for Einstein equations.

Abstract

In this work, we will explore the effects of F(R) 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 $N=6ABCD=6\eta^3D$ 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.