Non-Vacuum Bianchi Types I and V in f(R) Gravity

TL;DR

This paper extends previous vacuum solutions of Bianchi types I and V in f(R) gravity to include perfect fluid matter, deriving exact solutions that describe both singular and non-singular universe models and analyzing their physical properties.

Contribution

It introduces new exact solutions for Bianchi types I and V in f(R) gravity with perfect fluid matter, expanding the understanding of cosmological models in this framework.

Findings

Derived two exact solutions for each Bianchi type with perfect fluid

Identified models that are singular and non-singular

Analyzed physical behavior and Ricci scalar functions

Abstract

In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.