Constraining extended teleparallel gravity via cosmography: A model-independent approach

As a classical approach, the dynamics of the Universe, influenced by its dark components, are unveiled through prior modifications of Einstein's equations. Cosmography, on the other hand, is a highly efficient tool for reconstructing any modified theory in a model-independent manner. By employing kinematic variables, it offers a profound explanation for cosmic expansion. Although the cosmographical approach has been highly successful in several geometric theories in recent years, it has not been extensively explored in coupled gravities. With this in mind, we intend to constrain an extended teleparallel gravity model, $f(T,\mathcal{T})$, through cosmographic parameters. We utilize Taylor series expansion, assuming a minimally coupled form, to constrain the unknowns involved in the series. To achieve this, we conduct a Markov Chain Monte Carlo analysis (MCMC) using three different datasets (CC, BAO, and Pantheon+SH0ES). The constrained results obtained from MCMC are then compared and verified using various cosmological parameters. Finally, we compare the resulting models with \textbf{three} well-known $f(T,\mathcal{T})$ models.