Can we test Dark Energy with Running Fundamental Constants ?

We investigate a link between the running of the fine structure constant $\alpha$ and a time evolving scalar dark energy field. Employing a versatile parameterization for the equation of state, we exhaustively cover the space of dark energy models. Under the assumption that the change in $\alpha$ is to first order given by the evolution of the Quintessence field, we show that current Oklo, Quasi Stellar Objects and Equivalence Principle observations restrict the model parameters considerably stronger than observations of the Cosmic Microwave Background, Large Scale Structure and Supernovae Ia combined