Prospecting bipartite Dark Matter through Gravitational Waves

We explore the gravitational wave probes of a two-component dark matter framework, consisting of an $SU(2)_L$ triplet scalar and a Standard Model singlet fermion. The triplet scalar dark matter typically remains underabundant in the region below $\sim 1.9$ TeV, due to the strong $SU(2)_L$ gauge mediated interactions. We introduce a second dark matter component, an $SU(2)_L$ singlet vector-like Dirac fermion, to address this deficit in the dark matter relic abundance within a sub-TeV range. A key aspect of the proposed setup is the potential dark matter inter-conversion between the two components, which impacts the dark matter freeze-out dynamics and relic density of individual dark matter components. In such a scenario, we examine the properties of electroweak phase transition and identify the regions of parameter space that exhibit strong first-order phase transition. We estimate the resulting gravitational wave spectrum and its detectability, which could be probed through the conventional power-law-integrated sensitivity limits and the recently proposed peak-integrated sensitivity curves. Our analysis reveals that a novel region of the model's parameter space, compatible with dark matter observables, can generate a detectable gravitational wave spectrum, observable by upcoming space-based gravitational wave detectors such as LISA, BBO, DECIGO, and DECIGOcorr, while also offering complementary detection prospects in the dark matter and collider experiments.