Cosmological dynamics with nonlinear interactions

A non-gravitational, nonlinear interaction between dark matter and dark energy may result in a future evolution of the Universe which differs from that of the standard Lambda CDM model. In particular, the ratio of the energy densities of dark matter and dark energy may approach a stable finite value. For a special case, we find a corresponding analytic solution for the interacting two-component dynamics which is consistent with the supernova type Ia data from the Union2 set. For a broader class of interactions without analytic solutions, a dynamical system analysis classifies stationary points with emphasis on their potential relevance for the coincidence problem. Asymptotically stationary solutions of this kind require a phantom-type 'bare' equation of state of the dark energy which, however, does not lead to a big-rip singularity.