A comment on baryogenesis at the electroweak scale in alternative cosmologies

In this study we examine post-inflationary cosmologies dominated by a scalar field with the equation of state: p_phi=w_phi rho_phi (0 leq w_phi leq 1) in order to facilitate baryogenesis at the electroweak scale. We take a more conventional approach from one in Ref. 1 [Joyce, Prokopec] and assume that the Universe reheats by the scalar field decay before the nucleosynthesis epoch, and find a larger expansion rate at the electroweak scale than the one obtained in Ref. 1. The decaying field models suffer however from an entropy release that dilutes the baryon number produced at the electroweak scale. This dilution is minimized when the kinetic scalar field mode dominates (w_phi = 1), singling it out as the preferred cosmology with regard to baryogenesis. We study both cases, the electroweak transition with an expansion driven departure from equilibrium, and a first order phase transition. We show that in the former case with some tuning one can produce the amount of matter consistent with observation. In the latter case the expansion rate at the electroweak scale may be almost as large as the symmetric phase sphaleron rate, so that even the electroweak models with a relatively weak first order phase transition can be viable for baryogenesis.