POST INFLATIONARY BEHAVIOR OF STRING MODULI

We analyze the behaviour of moduli fields in string effective models b etween the end of inflation and reheating. The effective moduli potent ial during this era is derived for a class of simple models. We argue that this potential significantly stabilizes the modulus at its high e nergy minimum, if some restrictions on modular weights are met. Two me chanisms to further stabilize the moduli to their low energy minima ar e discussed explicitly: coinciding minima at a point of enhanced symme try, and the smooth transition from high to low energy minimum by an e ffective mass term (CH2)-H-2. For both cases we present explicit examp les, and C-2 is found to be O(10) at most. In addition, we show that d uring a smooth transition the reduction of the modulus amplitude stron gly depends on the shape of the low energy potential.