The simplest explanation for early time acceleration (inflation) and the late time acceleration indicated by recent data is that they have a common origin. We investigate another generic cosmological implication of this possiblity, that the baryon asymmetry of the universe may be generated in such models. We identify several novel features of baryogenesis in such a universe, in which a rolling scalar field is always part of the cosmological energy budget. We also propose a concrete mechanism by which the baryon asymmetry of the universe may be generated in this context. We analyze the generic properties of and constraints on these cosmologies, and then demonstrate explicitly how a complete cosmology may develop in some specific classes of models.

22 pages, 1 figure, uses RevTeX