Quantum Cosmology in Bergmann-Wagoner Scalar-tensor Gravitational Theory

Abstract

The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \lambda(\phi)=0, ii) \lambda(\phi)=3\Lambda_0\phi and iii) a more complex \lambda(\phi), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.