SIMBAD references

We investigate the viability of a modified teleparallel gravity model, specifically within the framework of $f(T)$ gravity, by implementing two complementary approaches for cosmological parameter estimation. In the first approach, we incorporate the $f(T)$ model into a Padé (2,1) parametrization of the Luminosity distance $d_\mathrm{ L}(z)$, enabling a stable and accurate description of the cosmic expansion history across redshift. In the second, we directly solve the modified first Friedmann equation arising from the same $f(T)$ model. Both approaches are subjected to a comprehensive Markov Chain Monte Carlo analysis using the latest cosmological observations, including cosmic chronometers, gravitational wave standard sirens, DESI BAO DR2, the Pantheon + SH0ES compilation, and Union3. We find that the parameter constraints obtained from the Padé-based formulation are in close agreement with those from the direct dynamical method, highlighting the internal consistency of the $f(T)$ scenario and the effectiveness of Padé expansions in confronting modified gravity theories with data. In fact, both methods exhibit a better fit than the standard lambda cold dark matter ($\Lambda$CDM) model in light of the DESI DR2 and Union3 observations. In addition, we present a detailed account of the Bayesian analysis methodology and compile a comprehensive set of the most recent and relevant cosmological data sets used in our study.