On the Expansion Rate of the Universe at the Electroweak Scale

A homogeneous mode of a scalar field in a “fast roll” (φ̇2 >> V (φ)), which has an energy density scaling as 1/a6 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 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 re-