Electroweak phase transition with composite Higgs models: calculability, gravitational waves and collider searches

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.