Electroweak Baryogenesis and the Expansion Rate of the Universe

A homogeneous mode of a scalar field in a ``fast roll'' ( \dot{\phi}^2 >> V(\phi)), which has an energy density scaling as 1/a^6 in an expanding universe, could dominate the universe at the electroweak epoch. The requirement that the energy in the mode red-shift away before nucleosynthesis gives a significantly weakened sphaleron bound for the preservation of a baryon asymmetry produced at a first-order phase transition. The observed baryon asymmetry might even be produced at the electroweak scale in the case that the phase transition is second-order or cross-over. A period where the energy in the universe is dominated by such a mode, which I term {\it kination}, can occur as a scalar field rolls down an exponential potential well motivated in many extensions of standard model physics. A cosmological ``constant'' at the present epoch may also result