Decoding cosmic acceleration through f(T) gravity: A Bianchi type-I perspective

This study explores cosmological dynamics in [Formula: see text] gravity within an anisotropic Bianchi type-I space–time using fractional linear varying deceleration parameter (FLVDP), with parameters constrained by 77 observational [Formula: see text] data points via [Formula: see text]-minimization, yielding [Formula: see text] [Formula: see text]km/s/Mpc at [Formula: see text] (13.8[Formula: see text]Gyr). We compare the linear [Formula: see text] model against a power-law form [Formula: see text], deriving analytical expressions for energy density, pressure, and the equation of state (EoS) parameter. Our results show that the power-law model produces a observationally consistent EoS value [Formula: see text], while the linear model exhibits phantom behavior with [Formula: see text]. The FLVDP framework accurately reproduces the deceleration-to-acceleration transition, with the power-law model exhibiting more gradual evolution, indicating torsion-based modifications regulate cosmic dynamics. This work establishes the power-law [Formula: see text] model in anisotropic space–time as a compelling alternative to standard cosmology, aligning better with both theoretical expectations and observational data.