Dynamical properties of scaling solutions in teleparallel dark energy cosmologies with nonminimal coupling

The dynamical aspects of scaling solutions for the dark energy component in the theoretical framework of teleparallel gravity are considered, where dark energy is represented by a scalar field nonminimally coupled with the torsion and with a boundary term, where the boundary coupling term represents the divergence of the torsion vector. The behavior and stability of the scaling solutions are studied for scalar fields endowed with inverse power law potentials and with exponential potentials. It is shown that for scalar fields endowed with inverse power-law potentials, the stability conditions are not affected by the coupling coefficients. For the scalar fields endowed with exponential potentials, two cases are studied: at first, we have considered an infinitesimal deviation from the scaling solution in the corresponding Klein-Gordon equation, and the impact of distinct coupling coefficients on the stability of the solution are analyzed. Secondly, the potential-free case is considered where the dominance of the coupling terms over the potential term is analyzed, discussing the validity of the corresponding particular solution.