Stability analysis of anisotropic Bianchi type-I cosmological model in teleparallel gravity

TL;DR

This paper investigates a Bianchi type-I cosmological model in teleparallel gravity, showing it transitions from deceleration to acceleration, and compares its predictions with observational data like supernovae.

Contribution

It introduces a new cosmological solution in teleparallel gravity with a linear deceleration parameter, analyzing its physical viability and consistency with observations.

Findings

Model transitions from deceleration to acceleration.

Consistent with supernova observational data.

Stable under energy conditions.

Abstract

In this work, we study a cosmological model of Bianchi type-I Universe in teleparallel gravity for a perfect fluid. To obtain the cosmological solution of the model, we assume that the deceleration parameter is a linear function of the Hubble parameter $H$ i.e. $q=-1+\beta H$ (where $\beta $ as a positive constant). Consequently, we get a model of our Universe, where it goes from the initial phase of deceleration to the current phase of acceleration. We have discussed some physical and geometric properties such as Hubble parameter, deceleration parameter, energy density, pressure, and equation of state (EoS) parameter and study their behavior graphically in terms of redshift and compare it with observational data such as Type Ia supernovae (SNIa). We also discussed the behavior of other parameters such as the Jerk parameter, Statefinder parameters and we tested the validity of the model by studying the stability analysis and energy conditions.