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We revisit the electroweak phase transition in the scalar singlet extensionof the standard model with a $\mathbb{Z}_2$ symmetry. In significant parts ofthe parameter space the phase transition occurs in two steps - includingcanonical benchmarks used in experimental projections for gravitational waves.Domain walls produced in the first step of the transition seed the final stepto the electroweak vacuum, an effect which is typically neglected but leads toan exponentially enhanced tunnelling rate. We improve previous results obtainedfor the seeded transition, which made use of the thin-wall or high temperatureapproximations, by using the mountain pass algorithm that was recently proposedas a useful tool for seeded processes. We then determine the predictions of theseeded transition for the latent heat, bubble size and characteristic timescale of the transition. Differences compared to homogeneous transitions aremost pronounced when there are relatively few domain walls per hubble patch,potentially leading to an enhanced gravitational wave signal. We also provide aderivation of the percolation criteria for a generic seeded transition, whichapplies to the domain wall seeds we consider as well as to strings andmonopoles.

Electroweak Phase Transition with a Double Well Done Doubly Well