On the avoidance of classical singularities in quantum cosmology

Abstract

Many cosmological models based on general relativity contain singularities. I address here the question whether consistent models without singularities can exist in quantum cosmology. The discussion is based on the Wheeler-DeWitt equation of quantum geometrodynamics. The models under consideration are partly motivated by recent discussions of dark energy. Natural criteria of singularity avoidance in the quantum theory are the vanishing of the wave function at the classical singularity or the breakdown of the semiclassical approximation upon approaching the region of the singularity. I show that singularity avoidance in this sense can happen in the models under consideration.