DILATON INDUCED QUANTUM INFLATION-COMPACTIFICATION AND POSSIBILITY OFTRANSITION TO CLASSICAL ERA

In many interesting models, including superstring theories, a vacuum w ith negative cosmological constant is predicted. For quantum cosmology (in higher dimensions) in the presence of coherent dilaton excitation s and a negative cosmological constant, the role of cosmic time can be understood and we can then predict the existence of a ''quantum infla tionary phase'' for some dimensions and a simultaneous ''quantum defla tionary phase'' for the remaining dimensions. We discuss qualitatively how it may be possible to exit from this inflation-compactification e ra and give an example which involves a transition to a phase with zer o cosmological constant which allows a classical description at late t imes.