Locally Rotationally Symmetric Bianchi Type $I$ Cosmology in $f(R,T)$ Gravity

TL;DR

This paper investigates Bianchi Type I cosmology within $f(R,T)$ gravity, deriving exact solutions under specific assumptions and analyzing physical quantities for each case.

Contribution

It provides new exact solutions for Bianchi Type I universe in $f(R,T)$ gravity using a specific proportionality assumption between expansion and shear.

Findings

Derived three exact solutions for the model.

Calculated physical quantities for each solution.

Explored implications of $f(R,T)$ gravity on anisotropic cosmology.

Abstract

This manuscript is devoted to investigate Bianchi Type $I$ universe in the context of $f(R,T)$ gravity. For this purpose, we explore the exact solutions of locally rotationally symmetric Bianchi type $I$ spacetime. The modified field equations are solved by assuming expansion scalar $\theta$ proportional to shear scalar $\sigma$ which gives $A=B^n$, where $A,\,B$ are the metric coefficients and $n$ is an arbitrary constant. In particular, three solutions have been found and physical quantities are calculated in each case.