Forbidden dark matter assisted by a first-order phase transition and the 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 underabundant relic and hence creating severe tension with cosmic microwave background (CMB) and indirect detection constraints. This is naturally remedied by a strong first-order phase transition (FOPT) in the dark sector, triggered by a scalar field Φ , which gives rise to masses for the dark gauge boson ( X D ) and the physical scalar ( ϕ ). To achieve the correct relic abundance while evading indirect detection constraints, the s -wave annihilation channel χ χ ¯ → X D ϕ is strictly maintained in the kinematically forbidden regime. Crucially, due to the U ( 1 ) D gauge structure, the usual χ χ ¯ → ϕ ϕ 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 χ χ ¯ → ϕ ϕ channel is also kinematically forbidden, it predominantly determines the relic density. Conversely, when the χ χ ¯ → ϕ ϕ channel is kinematically allowed, a rich interplay emerges between the tree-level forbidden χ χ ¯ → X D ϕ process and the loop-level allowed χ χ ¯ → ϕ ϕ 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 χ χ ¯ → ϕ ϕ final-state process, rendering the scenario entirely safe from CMB and indirect search bounds. Moreover, the same symmetry-breaking phase transition is strongly first-order, producing a stochastic gravitational-wave background that could be probed by upcoming space-based interferometers and pulsar timing arrays. We demonstrate that achieving the observed DM abundance tightly correlates the DM mass with the nucleation temperature of the phase transition. Thus, this setup links the DM relic abundance, dark-sector dynamics, and gravitational-wave signals, offering complementary paths to discovery in both terrestrial and cosmological observations.