Time-varying fine structure constant from naturally ultralight dark matter

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