Two Fluids in f(T) Gravity with Observational Constraints

Abstract

A locally rotationally symmetric Bianchi type-I model has been studied with two fluids within the framework of the $f\left(T\right)$ theory of gravity. Bianchi type-I is an immediate generalization of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. We have derived the exact field equations in $f\left(T\right)$ gravity by considering the Bianchi type-I metric and applying the action for $f\left(T\right)$ theory of gravity. We have utilized the torsion scalar $T$ and the Lagrangian for matter. The field equations are obtained by taking the variation of the action with respect to the vierbein, leading to a set of equations that includes the energy–momentum tensor for two fluid sources: matter and radiation. We fit the $H\left(z\right)$ curve using 57 data points and the $R^2$-test, achieving an $R^2$ value of 0.9321, indicating a strong fit with the Observational Hubble Dataset (OHD). Cosmological parameters like energy density, pressure, and state finder diagnostics are also discussed.