Dark photon oscillations in our inhomogeneous Universe

A dark photon kinetically mixing with the ordinary photon represents one of the simplest viable extensions to the standard model, and would induce oscillations with observable imprints on cosmology. Oscillations are resonantly enhanced if the dark photon mass equals the ordinary photon plasma mass, which tracks the free electron number density. Previous studies have assumed a homogeneous Universe; in this Letter, we introduce for the first time an analytic formalism for treating resonant oscillations in the presence of inhomogeneities of the photon plasma mass. We apply our formalism to determine constraints from cosmic microwave background photons oscillating into dark photons, and from heating of the primordial plasma due to dark photon dark matter converting into low-energy photons. Including the effect of inhomogeneities demonstrates that prior homogeneous constraints are not conservative, and simultaneously extends current experimental limits into a vast new parameter space.