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 \(\Lambda\)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 \(\Lambda\)CDM model for given observational data.