Rescuing Overabundant Dark Matter with a Strongly First Order Phase Transition in the Dark Sector

Abstract: We consider a dark sector consisting of fermionic dark matter (DM) charged under a broken dark $U(1)_D$ gauge symmetry, interacting with the Standard Model through kinetic mixing. In such models, the DM annihilation cross section is typically suppressed by the small kinetic mixing and or a heavy mediator, often leading to an overabundant relic density. We show that the observed DM abundance can be achieved if the dark Higgs undergoes a strong first order phase transition after DM freeze-out. In this scenario, the relic abundance is set by thermal freeze-out in the symmetric phase and subsequently reduced by entropy injection from the phase transition, rather than by annihilation in the broken phase. We find that to reproduce the observed relic abundance, the required phase transition is generically supercooled. The resulting stochastic gravitational wave signal lies within the sensitivity of future experiments, providing a complementary probe of this framework. Moreover, a strongly supercooled phase transition can potentially account for the NANOGrav signal for DM masses below $O(10)$ GeV.