Stationary dark energy: the present universe as a global attractor

We propose a cosmological model that makes a significant step toward solving the coincidence problem of the near similarity at the present of the dark energy and dark matter components. Our cosmology has the following properties: a) among flat and homogeneous spaces, the present universe is a global attractor: all the possible initial conditions lead to the observed proportion of dark energy and dark matter; once reached, it remains fixed forever; b) the expansion is accelerated at the present, as requested by the supernovae observations; c) the model is consistent with the large-scale structure and microwave background data; d) the dark energy and the dark matter densities always scale similarly after equivalence and are close to within two orders of magnitude. The model makes use of a non-linear coupling of the dark energy to the dark matter that switches on after structure formation.