A Time-Varying Fine Structure Constant from Naturally Ultralight Dark Matter

We present a class of models in which the coupling of the photon to an ultralight scalar field that has a time-dependent vacuum expectation value causes the fine structure constant to oscillate in time. The scalar field is assumed to constitute all or part of the observed dark matter. Its mass is protected against radiative corrections by a discrete $\mathbb{Z}_N$ exchange symmetry that relates the Standard Model to several copies to itself. The abundance of dark matter is set by the misalignment mechanism. We show that the oscillations in the fine structure constant are large enough to be observed in current and near-future experiments.