Inflationary Affleck-Dine scalar dynamics and isocurvature perturbations

We consider the evolution of the Affleck-Dine scalar during D-term and F-term inflation and solve the combined slow-roll equations of motion. We show that for a typical case, where both the Affleck-Dine scalar and inflaton initially have large values, in D-term inflation the Affleck-Dine scalar is driven to a fixed value, with only a very slight dependence on the number of e-foldings. As a result, there is a definite prediction for the ratio of the baryonic isocurvature perturbation to the adiabatic perturbation. In minimal $(d=4)$ Affleck-Dine baryogenesis the relative isocurvature contribution to the CMB angular power spectrum amplitude is predicted to be in the range 0.01--0.1, which can account for present large-scale structure observations and should be observable by Planck. In a very general case, scale invariance of the adiabatic perturbations from the Affleck-Dine scalar imposes a lower bound of about 0.01 for $d=4.$ For $d=6$ the isocurvature perturbation may just be observable, although this is less certain. We also consider F-term inflation and show that the magnitude of the baryonic isocurvature perturbation is fixed by the value of H during inflation. For typical values of H the isocurvature perturbation could be close to present observational limits.