Dynamical system analysis of dark energy models in scalar coupled Metric-Torsion theories

We study the phase-space dynamics of cosmological models in the theoretical formulations of nonminimal metric-torsion couplings with a scalar field, and investigate in particular the critical points (CPs) which yield stable solutions exhibiting cosmic acceleration driven by the dark energy (DE). The latter is so defined that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar-tensor cosmological setup, the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable CPs, we check their physical viability in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work [S. Sur and A. S. Bhatia, arXiv: 1611.00654 [gr-qc]]. We not only examine the regions of physical relevance in the phase-space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively noninteracting scenarios, in both Einstein and Jordan frames.