The Impossibility of Baryogenesis at a Second Order Electroweak Phase Transition

We investigate whether baryogenesis is possible at a second order electroweak phase transition. We find that under rather general conditions, the departure from thermal equilibrium is suppressed by the expansion rate of the Universe, and hence baryon production is also suppressed by the expansion rate. We conclude that if no additional sources of departure from thermal equilibrium such as topological defects are present, then electroweak baryogenesis is ruled out if the phase transition is second order or crossover. However, a non-vanishing net baryon to entropy ratio {\it is} generated, and we provide both upper and lower bounds for the result. Our technique is also applicable to other baryogenesis mechanisms taking place during and immediately after a second order phase transition. We estimate the lowest value of the transition energy scale for which the resulting baryon to entropy ratio might be large enough to explain observations.