Stationary dark energy with a baryon-dominated era: Solving the coincidence problem with a linear coupling

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We show that all cosmological models with an accelerated stationary global attractor reduce asymptotically to a dark energy field with an exponential potential coupled linearly to a perfect fluid dark matter. In such models the abundance of the dark components reaches a stationary value and therefore the problem of their present coincidence is solved. The requirement of a vanishing coupling of the baryons in order to pass local gravity experiments induces the existence of an intermediate baryon-dominated era. We discuss in detail the properties of these models and show that to accommodate standard nucleosynthesis they cannot produce a microwave background consistent with observations. We conclude that, among stationary models, only a time-dependent coupling or equation of state might provide a realistic cosmology.