Cosmological Problems in Supergravity in Inflationary Universe

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We have studied inflationary universe models in the framework of supergravity. We have solved initial value problem in a new inflation model introducing "pre-inflation" which takes place before the new inflation and sets the initial vale through supergravity effects. This "double inflation" model leads to production of primordial black holes or a broken power spectrum of density fluctuations. We have also studied a chaotic inflation model in supergravity which was difficult to construct a realistic model. By introducing a new symmetry we have successfully constructed a chaotic inflation model in supergravity. Furthermore, we have studied baryogenesis in SUSY models and, in particular, studied the dynamics of the Q-balls and Affleck-Dine field and have found that the model parameters are stringently constrained by the existence of the Q-ball. We have also considered the moduli problem in superstring theories and shown that the entropy production which is necessary to solve that problem is hardly consistent with baryogenesis.