Phase Space Dynamics of Non-Gravitational Interactions between Dark Matter and Dark Energy: The Case of Ghost Dark Energy

We study the phase space asymptotics of the so called Veneziano ghost dark energy models. Models where the ghost field's energy density: i) $\rho_{ghost}\propto H$, and ii) $\rho_{ghost}\propto H+H^2$, are investigated. Both, cases with and without additional non-gravitational interaction between cold dark matter and ghost dark energy, are subject to scrutiny. We pay special attention to the choice of phase space variables leading to bounded and compact phase space so that no critical point of physical interest is missing. A rich asymptotic structure is revealed: depending on the kind of non-minimal coupling critical points associated with radiation dominance, matter dominance, cold dark matter/ghost dark energy scaling, and ghost dark energy dominance, are found. Past and future attractors, as well as saddle equilibrium points, are identified in the corresponding phase spaces.