Exact Solutions of Bianchi Types $I$ and $V$ Spacetimes in $f(R)$ Theory of Gravity

TL;DR

This paper derives exact vacuum solutions for Bianchi types I and V spacetimes within $f(R)$ gravity, revealing models that are either singular or non-singular, and analyzing their physical properties and Ricci scalar functions.

Contribution

It presents two new exact solutions for Bianchi I and V spacetimes in $f(R)$ gravity using the variation law of Hubble parameter, including singular and non-singular models.

Findings

One solution is singular, the other is non-singular.

The models' physical behaviors are analyzed.

Ricci scalar functions are explicitly evaluated.

Abstract

In this paper, the crucial phenomenon of the expansion of the universe has been discussed. For this purpose, we study the vacuum solutions of Bianchi types $I$ and $V$ spacetimes in the framework of $f(R)$ gravity. In particular, we find two exact solutions in each case by using the variation law of Hubble parameter. These solutions 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 is discussed. Moreover, the function of the Ricci scalar is evaluated for both the models in each case.