QUANTUM COSMOLOGY IN THE MODELS OF 2D AND 4D DILATONIC SUPERGRAVITY WITH WZ MATTER - ART. NO. 084026

We consider N=1 two-dimensional (2D) dilatonic supergravity (SG), 2D d ilatonic SG obtained by dimensional reduction from N=1 four-dimensiona l (4D) SG, N=2 2D dilatonic SG, and string-inspired 4D dilatonic SG. F or all the theories, the corresponding action on a bosonic background is constructed and the interaction with N (dilatonic) Wess-Zumino mult iplets is presented. Working in the large-N approximation, it is enoug h to consider the trace anomaly induced effective action due to dilato n-coupled conformal matter as a quantum correction (for 2D models the s-wave approximation is additionally used), The equations of motion fo r all such models with quantum corrections are written in a form conve nient for numerical analysis. Their solutions are numerically investig ated for 2D and 4D Friedmann-Robertson-Walker or 4D Kantowski-Sacks un iverses with a time-dependent dilaton via exponential dilaton coupling . The evolution of the corresponding quantum cosmological models is gi ven for different choices of initial conditions and theory parameters. In most cases we find quantum singular universes. Nevertheless, there are examples of a universe nonsingular at early times. Hence, it look s unlikely that quantum matter back reaction on a dilatonic background (at least in large N approximation) may really help to solve the sing ularity problem. [S0556-2821(98)04718-3].