Electroweak Phase Transition in Two Scalar Singlet Model with pNGB Dark Matter

Abstract: We investigate the dynamics of the electroweak phase transition within an extended Standard Model framework that includes one real scalar $(\Phi)$ and one complex scalar $(S)$, both of which are SM gauge singlets. The global $U(1)$ symmetry is softly broken to a $\mathcal{Z}_3$ symmetry by the $S^3$ term in the scalar potential. After this $U(1)$ symmetry breaking, the imaginary component of the complex scalar $(S)$ acts as a pseudo-Nambu-Goldstone boson (pNGB) dark matter candidate, naturally stabilized by $\mathcal{Z}_2$ symmetry of the scenario. Specially, the spontaneous breaking of the global $U(1)$ symmetry to a discrete $\mathcal{Z}_3$ subgroup can introduce effective cubic terms in the scalar potential, which facilitates a strong first-order phase transition. We analyze both single-step and multi-step first-order phase transitions, identifying the parameter space that satisfies the dark matter relic density constraints, complies with all relevant experimental constraints, and exhibits a strong first-order electroweak phase transition. The interplay of these criteria significantly restricts the model parameter space, often leading to an under-abundant relic density. Moreover, we delve into the gravitational wave signatures associated with this framework, offering valuable insights that complement traditional dark matter direct and indirect detection methods.