Electroweak Baryogenesis and the Expansion Rate of the Universe

The standard requirement for the production of baryons at the electroweak phase transition, that the phase transition be first order and the sphaleron bound be satisfied, is predicated on the assumption of a radiation dominated universe at that epoch. One simple alternative-domination by the energy in a kinetic mode of a scalar field which scales as 1/a 6-gives a significantly weakened sphaleron bound for the preservation of a baryon asymmetry produced at a first-order phase transition, and allows the possibility that the observed baryon asymmetry be produced when the phase transition is second-order or cross-over. Such a phase of 'kination' at the electroweak scale can occur in various ways as a scalar field evolves in an exponential potential after inflation. The Hubble expansion rate H of a homogeneous and isotropic Big Bang universe is given by the very simple formula H 2 = (˙ a a) 2 = 8πG 3 ρ − k a 2 (1) where a is the scale factor, ρ is the energy density and k is a constant which depends on the spatial curvature [1]. The main contribution to ρ today comes from matter which scales as 1/a 3 , with perhaps also a curvature term and even a small cosmological (ρ =constant) 1 term. Going back in time the scale factor decreases and the energy density in the microwave background radiation blueshifts, scaling as 1/a 4 , until it comes to dominate the right hand