Abstract
The late-time acceleration of the universe remains one of the most significant open problems in modern cosmology. Modified gravity frameworks such as f( T) gravity provide a geometric alternative to dark energy by attributing cosmic acceleration to torsional effects. In this study, we present a comparative analysis of three different forms of f( T) models: (i) a simple power-law form f( T) = η( − T) n , (ii) the exponential form [Formula: see text], and (iii) a logarithmic form [Formula: see text]. Using parameterization of the deceleration parameter q( z) and the corresponding H( z) expression, we constrain the model parameters with the recent Hubble parameter and BAO data through a Markov Chain Monte Carlo approach. The physical behavior of the effective energy density, equation of state parameter, squared sound speed, cosmological Om( z) diagnostics, and energy conditions (null energy condition, dominant energy condition, and strong energy condition) were investigated for all three models. Our comparative analysis shows that all models asymptotically approach the ΛCDM behavior at late times, while they differ in stability properties and energy condition behaviors. In particular, the violation of the SEC has emerged as a common feature consistent with current accelerated expansion. This study highlights how different f( T) functional forms can yield distinct cosmological dynamics while maintaining consistency with observational data.