High Temperature Phase Transitions with the Effective Average Action

Abstract

According to the original argument of Kirzhnits and Linde [1] the electroweak symmetry is restored at temperatures much larger than the Fermi scale (=174 GeV). As the universe cooled after the big bang there must have been a phase transition from the symmetric to the spontaneously broken phase of the standard model. This phase transition may have many important consequences for our present universe, one example being the possible creation of the baryon asymmetry [2]. A reliable description of the electroweak phase transition cannot be obtained in the framework of the perturbative evaluation of the effective action [3, 4]. The reason is the appearance of infrared divergences at high orders of the perturbative expansion: corrections involving scalar fields are proportional to powers of λT/m s (T), which diverge near the critical temperature where m s (T cr ) = 0 [4]. If Goldstone modes are present their masses vanish at all temperatures in the spontaneously broken phase. Similarly loops with gauge fields involve powers of g 2 T/m A (T), which are problematic in the whole symmetric phase [5].