Gravitational waves and dark matter with Witten effect

Abstract: We investigate the breaking of dark $SU(2)_d$ symmetry at different temperature scales, occurring after Peccei-Quinn symmetry breaking or following QCD symmetry breaking. We focus on assessing the potential of the hidden monopoles generated during this process to serve as dark matter candidate. Additionally, we examine the impact of axion-monopole interactions on the axion mass. When the phase transition occurs at extremely high temperature ($\sim 10^8 \mathrm{GeV}$), the contribution of monopoles to the axion mass through witten effect becomes non-negligible, playing a crucial role in accurately determining the axion relic density. Moreover, the stochastic gravitational wave background generated by dark phase transition and axionic domain wall collapse may offer a potential explanation for the low-frequency gravitational wave signals observed in PTA experiments.