Plausible constraints and inflationary production for dark photons

Generic constraints on dark photons are generally presented assuming they have Stueckelberg masses. These constraints are strengthened if instead the mass is due to the Higgs mechanism and the dark Higgs is light. First, we show that under reasonable assumptions on the origin of kinetic mixing $\epsilon$ and perturbativity, the strengthened constraints on $\epsilon$ cannot be arbitrarily relaxed by making the Higgs heavy. Second, we demonstrate a simple mechanism for generating dark photon dark matter after inflation, where fluctuations of a dark Higgs by stochastic misalignment can produce stable dark photons through $h\to A'A'$ decay. Third, we point out new lower bounds on $\epsilon$ in the case where the dark photon mediates thermal freeze-out of light dark matter by $s$-channel exchange, taking account of generic expectations for the size of $\epsilon$, and astrophysical upper bounds on the self-interaction cross section.