Padé Cosmography and its insight into Teleparallel Gravity

Abstract 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 dL(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 ΛCDM 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 datasets used in our study.