Interacting Dark Matter and -Deformed Dark Energy Nonminimally Coupled to Gravity

In this paper, we propose a new approach to study the dark sector of the universe by considering the dark energy as an emerging q-deformed bosonic scalar field which is not only interacting with the dark matter, but also nonminimally coupled to gravity, in the framework of standard Einsteinian gravity. In order to analyze the dynamic of the system, we first give the quantum field theoretical description of the q-deformed scalar field dark energy and then construct the action and the dynamical structure of this interacting and nonminimally coupled dark sector. As a second issue, we perform the phase-space analysis of the model to check the reliability of our proposal by searching the stable attractor solutions implying the late-time accelerating expansion phase of the universe.