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

TL;DR

The work addresses the challenge of light dark matter by proposing a secluded dark sector in which a Dirac fermion χ annihilates predominantly through a forbidden channel χχ → X_D φ that becomes kinematically allowed after a strongly first-order U(1)$_D$ symmetry-breaking phase transition. This mechanism naturally suppresses late-time annihilations, satisfying CMB and indirect detection constraints, while the same phase transition sources a stochastic gravitational wave background detectable by current and future experiments. A tight link emerges between the DM mass M_χ and the nucleation temperature T_n of the phase transition, since the required mass splitting Δ and final-state masses scale with M_χ via v_φ, g_D, and λ_Φ. The framework yields concrete predictions for GW spectra, correlates DM phenomenology with dark-sector dynamics, and offers multiple experimental avenues for discovery, including PTA experiments, space-based GW detectors, and low-threshold DM searches.

Abstract

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.

Figures (6)

• Figure 1: Pictorial representation of our model, which gives rise to gravitational waves via a first-order phase transition and correct relic of DM through the forbidden channel.
• Figure 2: Allowed regions in the dark sector gauge coupling ($\textsl{g}_D$) vs scalar self-coupling ($\lambda_\phi$) plane for a fixed scalar vev $v_\phi = 500\,$MeV with the color scale representing the strength of the first-order phase transition (quantified by $\alpha$), with larger values indicating stronger transitions.
• Figure 3: Left: Dark matter relic density $\Omega_{\rm DM}h^2$ as a function of $\Delta$ for the benchmark points in Table \ref{['tab:tab1']}. Right: Evolution of the dark matter yield for BP2. The blue dashed line shows the equilibrium yield, while the blue solid line shows the actual yield when the relic abundance is set by the freeze-out of the forbidden process $\chi\bar{\chi}\rightarrow X_{D}\phi$ after the dark sector phase transition. The red solid line illustrates the under-abundant relic that would result for BP2 in the absence of the phase transition, where the same channel proceeds with effectively massless final-state particles.
• Figure 4: Parameter space in the $\epsilon$–$\Delta$ plane for BP1, BP2, BP3, and BP4 (top left, top right, bottom left, bottom right respectively), as defined in Table \ref{['tab:tab1']}. Shaded and hatched regions indicate different possible constraints; the vertical black dashed line shows the value of $\Delta$ yielding the correct dark matter relic abundance for each benchmark.
• Figure 5: Allowed parameter space from BBN and Higgs invisible decay constraints in the $\sin\theta$–$M_\phi$ plane. The gray shaded region is excluded because $\tau_\phi > \tau_{\rm BBN}$. The regions above the red lines are excluded by Higgs invisible decay bounds.