Gaussian superpositions in scalar-tensor quantum cosmological models - art. no. 083507

A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiti ng positive and negative frequency modes. The analysis is performed for pos itive, negative and zero values of the curvature of the spatial section. Ga ussian superpositions of the modes are constructed, and the quantum Bohmian trajectories are determined in the framework of the Bohm-de Broglie interp retation of quantum cosmology. Oscillating universes appear in all cases, b ut with a characteristic scale of the order of the Planck scale. Bouncing r egular solutions emerge for the flat curvature case. They contract classica lly from infinity until a minimum size, where quantum effects become import ant, acting as repulsive forces avoiding the singularity and creating an in flationary phase, expanding afterwards to an infinite size, approaching the classical expansion as long as the scale factor increases. These are nonsi ngular solutions which are viable models to describe the early Universe.