An Inflationary Non-singular Quantum Cosmological Model

Abstract

A stiff matter-dominated universe modeled by a free massless scalar field minimally coupled to gravity in a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry is quantized. Generalized complex-width gaussian superpositions of the solutions of the Wheeler-DeWitt equation are constructed and the Bohm-de Broglie interpretation of quantum cosmology is applied. A planar dynamical system is found in which a diversity of quantum bohmian trajectories are obtained and discussed. One class of solutions represents non-singular inflationary models starting at infinity past from flat space-time with Planckian size spacelike hypersurfaces, which inflates without inflaton but due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase.