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We propose a novel dark matter (DM) scenario based on a first-order phase transition in the early Universe. If dark fermions acquire a huge mass gap between true and false vacua, they can barely penetrate into the new phase. Instead, they get trapped in the old phase and accumulate to form macroscopic objects, dubbed Fermi-balls. We show that Fermi-balls can explain the DM abundance in a wide range of models and parameter space, depending most crucially on the dark-fermion asymmetry and the phase transition energy scale (possible up to the Planck scale). They are stable by the balance between fermion's quantum pressure against free energy release, hence turn out to be macroscopic in mass and size. However, this scenario generally produces no detectable signals (which may explain the null results of DM searches), except for detectable gravitational waves for electroweak scale phase transitions; although the detection of such stochastic gravitational waves does not necessarily imply a Fermi-ball DM scenario.

We study the strong first order electroweak phase transition (SFOEWPT) with the SO(6)/SO(5) composite Higgs model, whose scalar sector contains one Higgs doublet and one real singlet. Six benchmark models are built with fermion embeddings in 1, 6, and 15 of SO(6). We show that SFOEWPT cannot be triggered under the minimal Higgs potential hypothesis, which assumes the scalar potential is dominated by the form factors from the lightest composite resonances. To get a SFOEWPT, the contributions from local operators induced by physics above the cutoff scale are needed. We take the 6 + 6 model as an example to investigate the gravitational waves prediction and the related collider phenomenology. arXiv:1909.02014v2 [hep-ph] 5 Dec 2019 6 Which has been proved to be gauge-independent in Refs. [53,54]. 7 We briefly comment on the other two possible SFOEWPT mechanisms. The first one is the "one-step"

We study the complementarity of the proposed multi-TeV muon colliders and the near-future gravitational wave (GW) detectors to the first order electroweak phase transition (FOEWPT), taking the real scalar extended Standard Model as the representative model. A detailed collider simulation shows the FOEWPT parameter space can be greatly probed via the vector boson fusion production of the singlet, and its subsequent decay to the di-Higgs or di-boson channels. Especially, almost all the parameter space yielding detectable GW signals can be probed by the muon colliders. Therefore, if we could detect stochastic GWs in the future, a muon collider could provide a hopeful crosscheck to identify their origin. On the other hand, there is considerable parameter space that escapes GW detections but is within the reach of the muon colliders. The precision measurements of Higgs couplings could also probe the FOEWPT parameter space efficiently.