Quintessence Cosmology and Varying $α$

If dark energy is an ultra-light scalar field, or quintessence, then such a field could couple to ordinary matter, resulting in time variation of the constants of nature over cosmological time scales and the violation of the weak equivalence principle. Recent evidence for time variation of the fine structure constant $\alpha$ may be one of such signatures of quintessence. We point out that the observed $\dot\alpha$ could severely constrain the class of the quintessential potential. The future satellite experiment (STEP) should measure the induced violation of the weak equivalence principle.