Brans–Dicke versus f(T) gravity: Comparative insights into modified gravitational theories

This study performs a comparative cosmological analysis of Brans–Dicke theory (BDT) and [Formula: see text] gravity in the anisotropic Bianchi type-I spacetime. By using a hyperbolic sine form of the scale factor, we constrain the free parameters [Formula: see text] and [Formula: see text] against 77 [Formula: see text] data points via [Formula: see text] minimization, obtaining [Formula: see text] and [Formula: see text], with a reduced chi-square [Formula: see text]. The model predicts the present Hubble and deceleration parameters as [Formula: see text] and [Formula: see text], respectively. We derive and examine the dynamical evolution of energy density, pressure, and the equation of state (EoS) parameter. A key outcome is the marked difference in late-time behavior: the [Formula: see text] model exhibits stronger acceleration with an EoS parameter trending toward phantom regimes, whereas the BDT model shows a distinctive late-time re-acceleration phase driven by the scalar field dynamics. These results highlight how geometric and scalar-field modifications of gravity lead to observationally distinguishable cosmic evolution.