Non-vacuum Solutions of Bianchi Type VI_0 Universe in f(R) Gravity

TL;DR

This paper derives and analyzes two non-vacuum solutions for Bianchi type VI_0 universe in f(R) gravity, revealing different expansion behaviors and singularity properties depending on the matter content.

Contribution

It provides new exact solutions for Bianchi type VI_0 spacetime in f(R) gravity with isotropic and anisotropic fluids, exploring their physical and geometrical evolution.

Findings

Isotropic fluid model has a singularity at t=0 and enters a phantom phase.

Anisotropic fluid model has no initial singularity and shows uniform acceleration.

Spacetime remains anisotropic as t approaches infinity.

Abstract

In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI_0 spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the source of matter and dark energy. The physical behavior of these solutions is analyzed and compared in the future evolution with the help of some physical and geometrical parameters. It is concluded that in the presence of isotropic fluid, the model has singularity at $\tilde{t}=0$ and represents continuously expanding shearing universe currently entering into phantom phase. In anisotropic fluid, the model has no initial singularity and exhibits the uniform accelerating expansion. However, the spacetime does not achieve isotropy as $t\rightarrow\infty$ in both of these solutions.