Cosmology with Interaction between Phantom Dark Energy and Dark Matter and the Coincidence Problem

We study a cosmological model in which phantom dark energy is coupled to dark matter by phenomenologically introducing a coupled term to the equations of motion of dark energy and dark matter. This term is parameterized by a dimensionless coupling function $\delta$, Hubble parameter and the energy density of dark matter, and it describes an energy flow between the dark energy and dark matter. We discuss two cases: one is the case where the equation-of-state $\omega_e$ of the dark energy is a constant; the other is that the dimensionless coupling function $\delta$ is a constant. We investigate the effect of the interaction on the evolution of the universe, the total lifetime of the universe, and the ratio of the period when the universe is in the coincidence state to its total lifetime. It turns out that the interaction will produce significant deviation from the case without the interaction.