Factor ordering in standard quantum cosmology

Abstract

The Wheeler–DeWitt equation of Friedmann models with a massless scalar quantum field is formulated with arbitrary factor ordering of the Hamiltonian constraint operator. A scalar product of wavefunctions is constructed, giving rise to a probability interpretation and making comparison with the classical solution possible. In general the behaviour of the wavefunction of the model depends on a critical energy of the matter field which, in turn, depends on the chosen factor ordering. By certain choices of ordering the critical energy can be pushed down to zero. The essential features of the models, i.e. the dependence of the wavefunction on factor ordering and on the field energy, and the existence of a correct classical limit are the same for zero and nonzero cosmological constant.