The causal interpretation of conformally coupled scalar field quantum cosmology

We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfa ces have positive curvature. In order to symplify the system of coupled equ ations studied and study the quantum behavior near the singularity, we rest ricted ourselves to the cases where the scale factor is small. In this case , the general solution of the Wheeler-DeWitt equation is a discrete superpo sition of Hermitian polynomials multiplied by complex exponentials. Superpo sitions with up to two parcels are studied, and the phase diagrams of their corresponding Bohmian trajectories are analyzed in detail. Nonsingular per iodic quantum solutions are found. We also find that singular quantum solut ions present an inflationary era in the begining of the Universe. Numerical calculations indicates that these results remain valid for general superpo sitions.