Quantum cosmological singularities

Abstract

The problem of gravitationally induced spacetime collapse is studied in the framework of quantum cosmology. We find that whether quantum collapse occurs is effectively predetermined, on the classical level, by the choice of time. The crucial distinction is between "fast" and "slow" times, that is, between times which give rise to complete or incomplete classical evolution, respectively. We conjecture that unitary slow-time quantum dynamics is always nonsingular, while unitary fast-time quantum dynamics inevitably leads to collapse. These contentions are supported by an analysis of the dust-filled Friedmann-Robertson-Walker universes in two choices of time: a cosmic time defined by the velocity potential for the dust and an intrinsic time linked to the expansion. Indeed, these quantum models avoid the classical singularity in the slow matter-time gauge but collapse in the fast geometric-time gauge. We also investigate the qualitatively different forms---unitary and contractive---that the slow-time quantum evolution may take and explore their implications regarding quantum singularity avoidance. One surprising result is that, contrary to widespread belief, this phenomenon does not depend upon the choice of boundary conditions.