Probing the Electroweak Phase Transition in the Dark Sector

TL;DR

The paper investigates a minimal dark sector extension of the Standard Model featuring an SU(2)_D gauge group and a dark scalar doublet coupled to the Higgs via a portal. By scanning the parameter space under theoretical, collider, and astrophysical constraints and tracing the finite-temperature evolution of the scalar potential, it identifies regions that yield the observed DM relic density and strong first-order phase transitions that generate stochastic gravitational waves. The predicted GW signals, dominated by sound waves, fall within the reach of upcoming space-based detectors such as LISA, DECIGO, BBO, TianQin, and Taiji. The results illustrate the complementarity of gravitational-wave observations with traditional DM probes for testing dark-sector extensions of the Standard Model.

Abstract

We study an extension of the Standard Model with a dark SU(2) gauge group, where a dark scalar doublet interacts with the Standard Model Higgs through a portal coupling, inducing mixing after symmetry breaking. A custodial symmetry ensures the stability of the dark gauge bosons, making them viable dark matter candidates. Scanning the parameter space of the model under collider and astrophysical constraints, we find regions that yield the observed relic density and strong first-order phase transitions. The resulting gravitational-wave signals fall within the reach of upcoming space-based detectors.

Figures (5)

• Figure 1: Interaction between SM and Dark Sector
• Figure 2: Projections of the parameter space satisfying all constraints. Magenta points also reproduce the observed relic density within $3\sigma$, while grey points correspond to underabundant dark matter.
• Figure 3: Projection of the scanned parameter space onto the $\{m_{V_D}, m_{H_D}\}$ plane. The top panel shows the complete set of scan results, while the remaining panels display individual phase transition steps. The colour scale in each panel represents the phase transition strength parameter $\alpha$.
• Figure 4: The top panel presents how the phase-transition strength $\alpha$ varies with the inverse duration parameter $\beta/H_*,$ where the colour scale reflects the predicted DM abundance. In the bottom panel, the connection between the critical temperature $T_c$ and the nucleation temperature $T_n$ is shown, with the colour map representing the corresponding values of $\alpha$ and highlighting how the transition strength evolves with temperature.
• Figure 5: Peak GW energy density $h^2\Omega^{\text{peak}}_{\text{GW}}$ versus peak frequency $f^{\text{peak}}$. Darker points indicate parameter sets consistent with the observed dark matter relic density. Power-law integrated sensitivity curves for LISA, DECIGO, BBO, TianQin, and Taiji are shown.