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.

Figures (2)

• Figure 1: GW spectra generated by the dark Higgs first order phase transition for the benchmark scenarios BMA–BMD listed in Table \ref{['tab:BMs']}. Each panel corresponds to a different DM mass and model parameters as specified in the table. The GW signal is computed assuming a supercooled phase transition with phase transition temperature $T_*\simeq m_\psi/100$, $\alpha$ parameter $\alpha = 10$, bubble wall velocity $v_w=1$. The blue solid, red dashed, and green dotted curves correspond to different values of the mean bubble separation $R_*H_* = 10^{-1}$, $10^{-2}$, and $10^{-3}$ respectively. Projected sensitivity curves for future GW observatories, including THEIA 2018FrASS...5...11V, $\mu \rm{Ares}$Sesana:2019vho, LISA Caprini:2019egzamaro2017laserRobson:2018ifk, Taiji Ruan:2018tsw, TianQin TianQin:2015yph, DECIGO Kawamura:2020pcgKawamura:2006up, and BBO Corbin:2005nyYagi:2011wg are shown for comparison
• Figure 2: GW spectra from a supercooled dark Higgs phase transition for different DM masses and phase transition temperatures, overlaid with the NANOGrav 15-year data set NANOGrav:2023gor and the projected sensitivity of Gaia brown2018gaia, and THEIA 2018FrASS...5...11V. All spectra are computed assuming strong supercooling with $\alpha = 100$, relativistic bubble wall, $v_w\simeq 1$ and values of the mean bubble separation parameter $R_{*} H_{*}$ in the range $0.1$–$0.3$, as indicated. The phase transition temperature is assumed to be $T_{*} \simeq m_{\psi}/100$.