  Cosmological dark energy is a natural source of variation of the fine
structure constant. Using a model-independent approach we show that once
general assumptions about the alpha-varying interactions are made, astronomical
probes of its variation constrain the dark energy equation of state today to
satisfy -1 < w_f < -0.96 at 3-sigma and significantly disfavour late-time
changes in the equation of state. We show how dark-energy-induced spatial
perturbations of alpha are linked to violations of the Equivalence Principle
and are thus negligible at low-redshift, in stark contrast to the BSBM
theories. This provides a new test of dark energy as the source of alpha
variation.
