Phantom scalar field with arbitrary potential: accelerating scaling attractors

Abstract: In this article, we investigate the dynamics of a phantom scalar field with an arbitrary potential, focusing on accelerating scaling solutions of cosmological relevance. We consider both uncoupled and coupled cosmological scenarios. In the latter case, the coupling between phantom dark energy and dark matter is motivated by the warm inflationary paradigm, with the dissipation coefficient assumed to be either constant or variable. The evolution equations of our coupled and uncoupled cosmological models are written in the form of autonomous systems, whose stability is studied using methods of qualitative analysis of dynamical systems. For this analysis, the only requirement imposed on the phantom scalar-field potential is that a specific dynamical variable, defined in terms of the potential and its derivative, must be invertible. We show that the uncoupled phantom cosmological model cannot accommodate any accelerated scaling solution, while such solutions do exist in the coupled scenario, for both constant and variable dissipation coefficients. Although there is a limitation to these scaling solutions $-$ specifically, the current stage of accelerated expansion is not preceded by a long enough matter-dominated era $-$ our results show that the existence of a direct coupling between phantom dark energy and dark matter yields great potential for addressing the cosmic coincidence problem.