Multi-step phase transition and gravitational wave from general ${\mathbb{Z}}_2$ scalar extensions

Abstract

Multi-step phase transition provides a paradigm in which a broken symmetry during phase transition can be restored, enriching the phenomena of both dark matter and baryon asymmetry. We study the dynamics of the multi-step phase transition in the standard model extension with additional isospin $N$-plet scalar field $\hat{I}{¦}_2$ under a discrete ${\mathbb{Z}}_2$ symmetry. We find that the multi-step phase transition could be triggered if there is a moderately large coupling between the Higgs and the $\hat{I}{¦}_2$ and this coupling is required to be larger as the mass of the $\hat{I}{¦}_2$ and/or isospin increase. The first-order phase transition at the first (second) step can be realized by the thermal loop (tree-level barrier) effects. Thus it is more likely that a detectable spectrum of gravitational waves can be produced at the second step of the phase transition.

41 pages, 12 figures; Journal version