Analyzing the Bianchi Type-I Universe with a Special Form of Deceleration Parameter in f(T) Gravity

Abstract

This paper investigates the homogeneous and anisotropic Bianchi type-I spacetime within the framework of f(T) gravity theory, utilizing a quadratic equation of state and a specific deceleration parameter. In this paper, we employ Bayesian statistical methods, utilizing the Markov Chain Monte Carlo (MCMC) technique, to estimate model parameters such as ξ and the Hubble constant H₀ using the Cosmic Chronometers (CC) dataset. We conduct a thorough and detailed analysis of the model's behavior via energy density (ρ), pressure (p) anisotropic parameter (A_m) torsion scalar (T) deceleration parameter (q) a function of redshift z. The physical acceptance and stability of the model are examined by analyzing energy conditions and the squared sound speed. Furthermore, all cosmological parameters are graphically illustrated to enhance our understanding of the universe's expansion and evolutionary history. In addition, the diagnostic parameters are analyzed to assess the deviation of the obtained model from the Lambda Cold Dark Matter (ΛCDM) model and to classify dark energy models during the expansion. Finally, our obtained model represents the transition of the universe from an early deceleration phase to the recent accelerated expansion phase. The universe exhibits anisotropic characteristics at present but is expected to become isotropic in the future. Ultimately, the behavior of our model aligns with that of a quintessence dark energy model.