  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.
