Simple scalar-singlet extensions of the Standard Model with a (spontaneously broken) Z 2 symmetry allow for a strong first order electroweak phase transition, as sought in order to realize electroweak baryogenesis. However they generically also lead to the emergence of phenomenologically problematic domain walls. Here we present a framework with a real scalar singlet that features a different thermal history that avoids this problem by never restoring the Z 2 symmetry in the early universe. This is accomplished by considering D > 4 operators that emerge on general grounds, understanding the model as the low energy tail of a more complete theory, like for example in composite Higgs scenarios. Sticking to the latter framework, we present a concrete SO(6)/SO(5) composite realization of the idea. To this end, we additionally provide a complete classification of the structure of the Higgs potential (and the Yukawa couplings) in SO(6)/SO(5) models with fermions in the 1, 6, 15 or 20 of SO(6).

Simple scalar-singlet extensions of the Standard Model with a (spontaneously broken) Z2 symmetry allow for a strong first order electroweak phase transition, as sought in order to realize electroweak baryogenesis. However they generically also lead to the emergence of phenomenologically problematic domain walls. Here we present a framework with a real scalar singlet that features a different thermal history that avoids this problem by never restoring the Z2 symmetry in the early universe. This is accomplished by considering D > 4 operators that emerge on general grounds, understanding the model as the low energy tail of a more complete theory, like for example in composite Higgs scenarios. Sticking to the latter framework, we present a concrete SO(6)/SO(5) composite realization of the idea. To this end, we additionally provide a complete classification of the structure of the Higgs potential (and the Yukawa couplings) in SO(6)/SO(5) models with fermions in the 1, 6, 15 or 20′ of SO(6).