Affleck Dine leptogenesis via multiple flat directions

We investigate the Affleck-Dine mechanism when multiple flat directions have large values simultaneously. We consider in detail the case when both $LH_u$ and $H_uH_d$ flat directions are operative with a non-renormalizable superpotential. In case Hubble induced A-terms are present for these two flat directions, their initial values are determined completely by the potential and there are no ambiguities how they are mixed. Moreover, CP is violated even when the Hubble parameter is large due to the Hubble induced A-term and cross coupling in F-term, so that the lepton asymmetry is generated just after the end of inflation. As a result, compared with the case of single flat direction, the resultant lepton-to-entropy ratio is enhanced by a factor of $H_{osc}/m_{3/2}$, where $H_{osc}$ is the Hubble parameter at the onset of oscillation and $m_{3/2}$ is the gravitino mass. However, when Hubble induced A-terms do not exist, there remains indefiniteness of initial phases and CP is violated spontaneously by the phase difference between initial phase and potential minima of the hidden-sector induced A-terms. Therefore, CP-violation is not effective until the onset of the oscillation of scalar fields around the origin and there is suppression factor from thermal effect as is the case of single flat direction. In this case, the amplitude of baryon isocurvature perturbation imposes constraints on the model parameters.