Sakharov's Three Conditions Evaluated in a Contracting Phase

Sakharov's conditions for generating a baryon asymmetry are usually checked in an expanding universe. This paper checks them, with numbers, in the contracting phase that precedes a bounce. Baryon-number violation is supplied by electroweak sphaleron-like rates, Gamma_sph = 25 alpha_w^5 T with alpha_w = 1/30. The ratio of this rate to the magnitude of the Hubble rate is 7.32e+09 at 100 GeV and 7.32e+01 at 1e10 GeV; the two rates are equal near T = 7.32e+11 GeV. Departure from equilibrium, the third condition, behaves differently under contraction: processes fall out of equilibrium as the temperature rises toward the bounce rather than as it falls, so the ordering of production and freeze-out is reversed relative to the expanding case. The first two conditions, baryon violation and CP violation, are properties of the particle physics and are unchanged by the sign of the expansion. The conclusion is that a contracting phase can satisfy all three conditions, but any asymmetry it produces must then run the gauntlet of the bounce itself. Computed, not measured.