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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. The $U(1)_D$ is spontaneously broken by a scalar field $Φ$, giving mass to the dark gauge boson $X_D$. The dominant DM annihilation proceeds via a forbidden channel, where the DM pair annihilates into slightly heavier dark gauge bosons and scalars after the dark-sector phase transition. Once the dark-sector phase transition occurs, the induced mass gap activates the forbidden annihilation channel, which in turn determines the DM relic abundance and naturally suppresses late-time annihilation. As a result, the scenario avoids stringent cosmic microwave background and indirect detection constraints that typically exclude thermal light DM. 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 for discovery in both terrestrial and cosmological observations.