Gravitational waves and dark matter with Witten effect*

Abstract We present an investigation on cosmological implications resulting from spontaneous dark symmetry breaking in conjunction with the Witten effect. Furthermore, we examine the mass of hidden monopoles generated by phase transition as well as the impact of axion-monopole interactions on the axion mass. Following spontaneous breaking of the PQ symmetry, axions emitted by cosmic strings or domain walls as well as hidden monopoles generated during this transition may collectively contribute to the observed dark matter relic density. Additionally, the stochastic gravitational wave background generated by sub-GeV phase transitions and by the decay of axionic domain walls formed during sub-ZeV phase transitions could account for the low-frequency gravitational wave signals detected by PTA experiments.