Singularities in a Scalar Field Quantum Cosmology

The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as source is further investigated. The classical model is singular, and in the framework of the Arnowitt-Deser-Misner canonical quantization formalism a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a matter-time gauge such that time is identified with the scalar field the classical model is singular either at $t=-\mathrm{\infty }$ or at $t=+\mathrm{\infty }$, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time.