Resolving FLRW Cosmology Through Effective Equations of State in f (T) Gravity

This article explores the cosmological scenario of the universe in the context of the f (T) power law model, where T represent the torsion scalar. To obtain the deterministic solution of the field equations we parametrized the effective Equation-of-State with two parameters m and k as suggested by A. Mukherjee in a flat FLRW environment. We impose constraints on the free parameters of the derived solution by utilizing MCMC analysis assuming the CC, Pantheon+SH0ES, and CC+Pantheon+SH0ES as data samples. We explore the dynamics of cosmological parameters. The evolutionary profile of the deceleration parameter exhibits the transition %from the decelerated to the accelerated phase. The effective Equation-of-State parameter indicates the model remains in the quintessence era and gradually becomes the Einsteins-de-Sitter model. In addition to this, we also explore the jerk, snap, and lerk parameters. Furthermore, the Om (z) diagnostic shows that the model has a consistent positive slope across the entire evolution, but resembles the standard CDM model in the near future. At last, we conclude that the power law function of the modified f (T) gravity model in the framework of the FLRW universe aligns more closely with the CDM model for given observational data.