Quantized Matter Fields and the Avoidance of Singularities in General Relativity

We consider a classical gravitational field minimally coupled to a quantized neutral scalar field possessing mass. We are especially concerned with the effects of particle creation and quantum coherence on the premises and conclusions of the singularity theorems, which imply the inevitability of singularities in classical general relativity. A closed Robertson-Walker geometry is used throughout. Nongravitational interactions are not considered. The source of the gravitational field in the Einstein equations is the expectation value of the energy-momentum tensor of the quantized scalar field. Lacking a general prescription for obtaining a finite operator from the divergent formal expression for the energy-momentum tensor, we confine our attention to situations in which plausible special methods are available. We show that quantum coherence effects in this semiclassical model can result in a violation of the energy conditions which enter into the singularity theorems. Then we exhibit numerical solutions of the coupled Einstein and scalar field equations in which a Friedmann-like collapse is stopped and converted to a Friedmann-like expansion. (In this calculation one mode of the quantum field was assumed dominant.) We conclude that quantum effects of the type considered here can sometimes lead to avoidance of the cosmological singularity, at least on the time scale of one Friedmann expansion.