A Confining Strong First-Order Electroweak Phase Transition

In the Randall-Sundrum model where the radion is stabilized by a Goldberger-Wise (GW) potential there is a supercooled transition from a deconfined to a confined phase at temperatures orders of magnitude below the typical Standard Model critical temperature. When the Higgs is localized at the IR brane the electroweak phase transition is delayed and becomes a strong first-order one where the Universe expands by a few e-folds. This generates the possibility of having the out-of-equilibrium condition required by electroweak baryogenesis in the electroweak phase transition. We have studied numerically the region of the GW parameter space where the theory is consistent and the latter possibility is realized. We have found that in most of the parameter space the nucleation temperature is so low that sphalerons are totally inactive inside the bubbles. The condition for sphalerons to be inactive after reheating imposes an upper bound on the reheating temperature that is weaker for heavy Higgs bosons so that the out-of-equilibrium condition seems to favor heavy over light Higgses. The condition for sphalerons to be active outside the bubbles puts an upper bound on the number of e-folds at the phase transition, roughly consistent with the critical value required by low-scale inflation to solve the cosmological horizon problem.