QUANTUM COSMOLOGY OF SUPERSTRING UNIVERSE

We study the quantum cosmology of the string universe obtained by embedding the Robertson-Walker metric in the nonlinear sigma-model 1. We find that the quantum model has some unusual features not seen in the classical model. Initially the universe exists in a series of metastable bound states with scale factor taking discrete values. Then the universe tunnels through a barrier and comes out in an inflationary state. This tunneling (or evolution in imaginary time) also has the effect of heating up the matter field so that we have the conditions of chaotic inflation. Our asymptotic solutions agree with those obtained from the classical Einstein equations in Ref. 1.