document: There are many possible applications for this mechanism. In this Letter, we have concentrated on its contribution to leptogenesis and baryogenesis. Our calculation is applicable in the phase when the fields are rolling. This rolling phase will start when the Hubble constant drops to a value comparable to the mass of the scalar fields. It is at this time in the cosmological evolution that CP violation is most efficient. After the fields have relaxed to their vacuum values, our CP violation mechanism turns off. We plan to discuss more details, in particular applications to concrete baryogenesis models, in a future publication [20]. Note that string cosmology and brane world scenarios may provide natural settings for the origin of the scalar fields required for our mechanism (e.g. see Ref. [30] for a recent paper on how scalar fields from brane world scenarios can play a new role in spontaneous baryogenesis).
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