Broken symmetries at high temperature

We have examined the high-temperature behavior of softly broken symmetries such as gauge invariance as well as parity and time-reversal invariance in a class of models of quantum flavor dynamics. We find that there exist domains of coupling parameters of the theory, for which the above symmetries remain broken 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. The fermion and boson masses in these models increase with temperature. A signature for such models is the existence of heavy Higgs bosons (with $m_H\gtrsim m_W$).