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A minimal extension of the Standard Model that provides both a dark mattercandidate and a strong first-order electroweak phase transition (EWPT) consistsof two additional Lorentz and gauge singlets. In this paper we work out acomposite Higgs version of this scenario, based on the coset $SO(7)/SO(6)$. Weshow that by embedding the elementary fermions in appropriate representationsof $SO(7)$, all dominant interactions are described by only three freeeffective parameters. Within the model dependencies of the embedding, thetheory predicts one of the singlets to be stable and responsible for theobserved dark matter abundance. At the same time, the second singlet introducesnew $CP$-violation phases and triggers a strong first-order EWPT, makingelectroweak baryogenesis feasible. It turns out that this scenario does notconflict with current observations and it is promising for solving the darkmatter and baryon asymmetry puzzles. The tight predictions of the model will beaccessible at the forthcoming dark matter direct detection and gravitationalwave experiments.

A unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures