Progress in the Theory of the Electroweak Phase Transition
  Recent progress in the theory of the electroweak phase transition is discussed. For the Higgs boson mass smaller than the masses of W and Z bosons, the phase transition is of the first order. However, its strength is approximately 2/3 times less than what follows from the one-loop approximation. This rules out baryogenesis in the minimal version of the electroweak theory with light Higgs bosons. The possibility of the strongly first order phase transition in the theory with superheavy Higgs bosons is considered.   We show that if the Yang-Mills field at high temperature acquires a magnetic mass $\sim g^2 T$, then no linear terms appear in the effective potential in all orders of perturbation theory and the symmetry in gauge theories at high temperatures is actually restored. Even though the last statement was never questioned by most of the authors, it was extremely difficult to come to a reliable conclusion about it due to the infrared problem in thermodynamics of non-Abelian gauge fields.   The phase transition occurs due to production and expansion of critical bubbles. A general analytic expression for the probability of the bubble formation is obtained, which may be used for study of tunneling in a wide class of theories. 
Andrei Linde