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A bstract Electroweak baryogenesis is an attractive mechanism to generate the baryon asymmetry of the Universe via a strong first order electroweak phase transition. We compare the phase transition patterns suggested by the vacuum structure at the critical temperatures , at which local minima are degenerate, with those obtained from computing the probability for nucleation via tunneling through the barrier separating local minima. Heuristically, nucleation becomes difficult if the barrier between the local minima is too high, or if the distance (in field space) between the minima is too large. As an example of a model exhibiting such behavior, we study the Next-to-Minimal Supersymmetric Standard Model, whose scalar sector contains two SU(2) doublets and one gauge singlet. We find that the calculation of the nucleation probabilities prefers different regions of parameter space for a strong first order electroweak phase transition than the calculation based solely on the critical temperatures. Our results demonstrate that analyzing only the vacuum structure via the critical temperatures can provide a misleading picture of the phase transition patterns, and, in turn, of the parameter space suitable for electroweak baryogenesis. 

A bstract 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.