Evolution of the Hubble Parameter in Non-Linear f ( T ) Theory of Gravity

We study late time cosmology in the teleparallel framework using a simple and data driven form of the Hubble rate, [Formula: see text]. We test nonlinear model [Formula: see text]. This setup keeps the background fully analytic and gives closed expressions for [Formula: see text], [Formula: see text], and [Formula: see text]. We fit the model to 57 observational Hubble measurements and to the Pantheon supernova sample and obtain tight best fit values for [Formula: see text] and [Formula: see text]. The model follows the observed rise of [Formula: see text] up to [Formula: see text] and matches the distance modulus over the full range. The deceleration parameter shows the expected change of sign. The transition redshift is [Formula: see text] for the Hubble data and [Formula: see text] for the Pantheon data. Today we find [Formula: see text], which confirms ongoing acceleration. The Om diagnostic is nearly constant near [Formula: see text] and close to the [Formula: see text]CDM value. It changes only mildly at higher redshift and shows no unphysical features. The pressure is negative at late times and the energy condition combinations behave in a regular way. This is consistent with an accelerating effective fluid. Information criteria such as AIC and BIC prefer [Formula: see text]CDM for the same Hubble set, but our teleparallel models still track the data well and allow controlled departures at earlier epochs. Overall, this framework gives a compact and clear description of cosmic acceleration that agrees with present data.