Electroweak $\!$phase $\!$transition $\!$with $\!$spontaneous $\!$$Z_2$-breaking

This work investigates a simple, representative extension of the Standard Model with a real scalar singlet and spontaneous $Z_2$ breaking, which allows for a strongly first-order phase transition, as required by electroweak baryogenesis. We perform analytical and numerical calculations that systematically include one-loop thermal effects, Coleman-Weinberg corrections, and daisy resummation, as well as evaluation of bubble nucleation. We study the rich thermal history and identify the conditions for a strongly first-order electroweak phase transition with nearly degenerate extrema at zero temperature. This requires a light scalar with mass below 50 GeV. Exotic Higgs decays, as well as Higgs coupling precision measurements at the LHC and future collider facilities, will test this model. Additional information may be obtained from future collider constraints on the Higgs self-coupling. Gravitational-wave signals are typically too low to be probed by future gravitational wave experiments.