Dynamical Theory of Phase Transitions and Topological Defect Formation in the Early Universe

We review the current issues of nonequilibrium phase transitions, in particular, in the early universe. Phase transitions cannot maintain thermal equilibrium and become nonequilibrium when the thermal relaxation time scale is greater than the dynamical time scale. Nonequilibrium phase transitions would have happened in certain evolution stages of the early universe because the rapid expansion quenched matter fields. We apply the recently introduced Liouville-von Neumann method, another canonical method, to nonequilibrium phase transitions in the Minkowski spacetime and find the scaling behavior of domain sizes. Topological defects are thus determined by the dynamical processes of nonequilibrium phase transitions. However, the expansion of the universe freezes domain growth in the comoving frame and thus leads to a scale-invariant domain size. We also discuss the physical implications of nonequilibrium phase transitions in the early universe.