Wormholes, classical limit and dynamical vacuum in quantum cosmology

First a Friedmann-Robertson-Walker (FRW) universe fined with dust and a con formally invariant scalar field is quantized. For the closed model we find a discrete set of wormhole quantum states. In the case of flat spacelike se ctions we find states with classical behaviour at small values of the scale factor and quantum behaviour for large values of the scare factor. Next we study a FRW model with a conformally invariant scalar field and a nonvanis hing cosmological constant dynamically introduced by regarding the vacuum a s a perfect fluid with equation of state p = -rho. The ensuing Wheeler-DeWi tt equation turns out to be a bona fide Schrodinger equation, and we find t hat there are realizable states with a definite value pf the cosmological c onstant. Once again we find finite-norm solutions to the Wheeler-DeWitt equ ation with definite values of the cosmological constant that represent worm holes, suggesting that in quantum cosmological models with a simple matter content wormhole states are a common occurrence.