A bound on light dark photon dark matter

We derive a bound on dark photon dark matter scenarios where the dark photon mass is generated through the Higgs mechanism, based on the requirement that symmetry breaking must occur sufficiently early in the universe. We emphasize that dark photon production occurs successfully when the dark Higgs field remains in the symmetric phase due to non-thermal trapping effects. For renormalizable Higgs potentials, our bound reads$\frac{m_{{\gamma }^{\prime }}}{q_H{e}_H}\gg 60\mathrm{eV}{\left(\frac{2\pi }{\lambda }\right)}^{1/4}$ where $m_{{\gamma }^{\prime }}$ is the dark photon mass, $e_H$ is the gauge coupling, $q_H$ is the charge of the dark Higgs boson, and λ is the Higgs quartic coupling. This constraint holds independently of any complications arising from the Schwinger effect and vortex formation in the Higgsed phase. For more general Higgs potentials such as the Coleman-Weinberg type potential, our bound yields different forms. We argue that late-time symmetry breaking of the dark U(1) symmetry satisfying our bound has only a mild impact on both the abundance and momentum distribution of dark photon dark matter, and therefore does not pose any serious problem for the dark photon dark matter scenario.