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; (c) the model is consistent with the large-scale structure and microwave background data; (d) the dark energy and the dark matter densities scale similarly after equivalence and are close to within one order of magnitude.