Cosmological and Dynamical Aspects of Teleparallel Gravity and its Extension (2510.02491v1)

Abstract: This thesis investigates the characteristics of modified teleparallel gravity models that incorporate a scalar field and a trace of the energy-momentum tensor, with particular attention to their cosmological effects, especially regarding late-time cosmic acceleration. Teleparallel gravity, as an alternative framework to General Relativity, defines gravity through torsion rather than curvature, and when combined with a scalar field, it allows exploration of a wider variety of cosmological scenarios. This thesis examines the late-time acceleration of the Universe and its various phases through dynamical system analysis within the framework of modified teleparallel gravity theories. It presents the mathematical formulations of $f(T)$, $f(T, \mathcal{T})$, $f(T, \phi)$, Horndeski teleparallel gravity, and the quintessence dark energy model, along with the application of dynamical systems and relevant cosmological datasets. Overall, the results demonstrate that these modified teleparallel gravity models provide viable descriptions of the late-time cosmic acceleration and offer insights into the dynamics of the Universe beyond standard cosmology.