SoftCP-Invariance Violation at High Temperature

We study the temperature dependence of soft $\mathrm{CP}$-invariance violation in a class of gauge theories based on the gauge group $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ and show that there exist physically acceptable domains of coupling parameters of the theory where $\mathrm{CP}$-invariance violation persists at high temperatures. Such models have the potential to explain matter-antimatter asymmetry in the universe while at the same time providing a cure for the strong $\mathrm{CP}$ problem.