Can we test dark energy with running fundamental constants?

We investigate a link between the running of the fine structure constant α and a time evolving scalar dark energy field. Employing a versatile parametrization for the equation of state, we exhaustively cover the space of dark energy models. Under the assumption that the change in α is to first order given by the evolution of the quintessence field, we show that current Oklo, quasi-stellar object and equivalence principle observations restrict the model parameters considerably more strongly than observations of the cosmic microwave background, large scale structure and supernovae Ia combined.