Dynamics of dark energy with a coupling to dark matter

Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modeled as exponential quintessence and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.

Figure 1

The region of stability (blue, shaded) in the $(b,\beta )$ parameter space, for critical point $D$ in coupling model (I).

Figure 2

The region of stability (blue, shaded) in the $(\lambda ,\alpha )$ parameter space, for critical point $D$ in coupling model (II).

Figure 3

Phase-space trajectories for coupling model (III), with $\lambda =1$ and $\gamma ={10}^{-6}$. The right-hand plot is the projection. The global attractor $G$ (see Table ) is apparent.

Figure 4

Phase-space trajectories for coupling model (III), with $\lambda =4$ and $\gamma ={10}^{-6}$. This plot shows the attractor $E$.