Gravitational Wave Signals of Electroweak Phase Transition Triggered by Dark Matter

TL;DR

The paper explores a SM extension with a scalar singlet dark matter candidate and an additional scalar mixing with the Higgs to realize a two-step electroweak phase transition, where the barrier between vacua appears at tree-level. This setup can yield a strongly first-order EWPT while accommodating a viable dark matter relic density and suppressing direct detection via mediator cancellations. The second-step transition generates gravitational waves whose spectrum can fall within the sensitivity of future space-based detectors such as eLISA, BBO, and DECIGO, offering a testable link between dark matter and baryogenesis. Overall, the work demonstrates a coherent DM–EWPT framework with observable gravitational wave signatures and delineates regions of parameter space that satisfy relic density, direct-detection, and phase-transition requirements.

Abstract

We study in this work a scenario that the universe undergoes a two step phase transition with the first step happened to the dark matter sector and the second step being the transition between the dark matter and the electroweak vacuums, where the barrier between the two vacuums, that is necessary for a strongly first order electroweak phase transition (EWPT) as required by the electroweak baryogenesis mechanism, arises at the tree-level. We illustrate this idea by working with the standard model (SM) augmented by a scalar singlet dark matter and an extra scalar singlet which mixes with the SM Higgs boson. We study the conditions for such pattern of phase transition to occur and especially for the strongly first order EWPT to take place, as well as its compatibility with the basic requirements of a successful dark matter, such as observed relic density and constraints of direct detections. We further explore the discovery possibility of this pattern EWPT by searching for the gravitational waves generated during this process in spaced based interferometer, by showing a representative benchmark point of the parameter space that the generated gravitational waves fall within the sensitivity of eLISA, DECIGO and BBO.

Figures (4)

• Figure 1: Results from a scan over the parameter space in plane $(m_S, \lambda_1)$ for the left panel and $(\theta, \lambda_1)$ for the right panel. Every point in these plots generates the desired EWPT pattern and leads to vanishing DM nucleon scattering cross section at tree level. The green points further gives DM relic density within the interval $\Omega_c h^2\in (0.03, 0.12)$. The red points, in addition to generating relic density falling into this interval, also satisfy the strong first order EWPT condition $v_h(T_C)/T_C \gtrsim 1$.
• Figure 2: This figure gives an illustrative picture of the two step EWPT with the first step in the $s$ direction and the subsequent one from $s$ direction to the $(h,\phi)$ direction.
• Figure 3: The left panel shows the evolution of $V$ at the two minima in $s$(blue) and in $(h,\phi)$(magenta dashed) directions as $T$ drops from right to left. The right panel shows the tracks of the minimum (blue dotted line) in the $(h,\phi)$ direction for the thermal history with the contours denoting the values of $V$ at $T=0$. In these plots, the magenta, blue, black and red dots represent the temperatures at $T_s=150\text{GeV}$, $T_h=108\text{GeV}$, $T_C=78.8\text{GeV}$ and $T=0$ respectively. The parameters are chosen as: $v_{\Phi} = 65\text{GeV}$, $m_{\hat{\phi}}=82\text{GeV}$, $m_S=71\text{GeV}$, $\lambda_S=0.015$, $\theta=0.12$, $\lambda_1=0.046$ and $\lambda_{3} = 0.57$ which gives $v_h(T_C)/T_C = 2.6$.
• Figure 4: The left panel shows changes of $S(T)/T$ in the neighborhood of $T_n$ and the right panel shows the GWs generated during the first order EWPT as a function of frequency from three sources: sound waves(blue dotdashed line), collision(red dotted line), turbulence(green dashed line) and total contribution(cyan solid line). The color shaded regions fall within the experimental sensitivities of eLISA(four configurations with notation NiAjMkLl), ALIA(gray), BBO(green), DECIGO(yellow) and Ultimate-DECIGO(purple).