Dark photon dark matter from cosmic strings and gravitational wave background

Dark photon dark matter may be produced by the cosmic strings in association with the dark U(1) gauge symmetry breaking. We perform three-dimensional lattice simulations of the Abelian-Higgs model and follow the evolution of cosmic strings. In particular, we simulate the case of (very) light vector boson and find that such vector bosons are efficiently produced by the collapse of small loops while the production is inefficient in the case of heavy vector boson. We calculate the spectrum of the gravitational wave background produced by the cosmic string loops for the light vector boson case and find characteristic features in the spectrum, which can serve as a probe of the dark photon dark matter scenario. In particular, we find that the current ground-based detectors may be sensitive to such gravitational wave signals and also on-going/future pulsar timing observations give stringent constraint on the dark photon dark matter scenario.