Non-thermally trapped inflation by tachyonic dark photon production

We show that a dark Higgs field charged under U(1)$_{\rm H}$ gauge symmetry is trapped at the origin for a long time, if dark photons are produced by an axion condensate via tachyonic preheating. The trapped dark Higgs can drive late-time inflation, producing a large amount of entropy. Unlike thermal inflation, the dark Higgs potential does not have to be very flat, because the effective mass for the dark Higgs is enhanced by large field values of dark photons with extremely low momentum. After inflation, the dark Higgs decays into massive dark photons, which further decay into the SM particles through a kinetic mixing. We show that a large portion of the viable parameter space is within the future experimental searches for the dark photon, because the kinetic mixing is bounded below for successful reheating. We also comment on the Schwinger effect which can hamper the tachyonic production of dark photons, when the mass of dark photon is not the St\"{u}ckelberg mass, but is generated by the Higgs mechanism. Such non-thermal trapped inflation could be applied to other cosmological scenarios such as the early dark energy, known as one of the solutions to the Hubble tension.