Forbidden dark matter assisted by first-order phase transition and associated gravitational waves

We propose a simple yet testable framework for light fermion dark matter (DM) with mass in the MeV--GeV range, charged under a dark $U(1)_D$ gauge symmetry. Before symmetry breaking, DM annihilates excessively into massless dark gauge bosons, resulting in an under-abundant relic and hence creating severe tension with cosmic microwave background (CMB) and indirect detection constraints. This is naturally remedied by a strongly first-order phase transition (FOPT) in the dark sector, triggered by a scalar field $\Phi$, which gives rise to masses for the dark gauge boson ($X_D$) and the physical scalar ($\phi$). To achieve the correct relic abundance while evading indirect detection constraints, the $s$-wave annihilation channel $\chi\bar{\chi} \rightarrow X_D \phi$ is strictly maintained in the kinematically forbidden regime. Crucially, due to the $U(1)_D$ gauge structure, the usual $\chi\bar{\chi} \rightarrow \phi\phi$ annihilation is strictly absent at tree level and only arises at the one-loop level. Within this framework, we explore two distinct possibilities. When the loop-induced $\chi\bar{\chi} \rightarrow \phi\phi$ channel is also kinematically forbidden, it predominantly determines the relic density. Conversely, when the $\chi\bar{\chi} \rightarrow\phi\phi$ channel is kinematically allowed, a rich interplay emerges between the tree-level forbidden $\chi\bar{\chi} \rightarrow X_D \phi$ process and the loop-level allowed $\chi\bar{\chi} \rightarrow\phi\phi$ process, with the dominant contribution being dictated sensitively by the DM mass and gauge coupling. The late-time annihilations are highly suppressed in both of these channels, either by the energetic threshold of the forbidden channel or the $p$-wave velocity suppression of the loop-induced $\chi\bar{\chi} \rightarrow\phi\phi$ final state process, rendering the scenario entirely safe from CMB and indirect search bounds...