Nonsingular general-relativistic cosmologies

Abstract

According to the "singularity theorems" of Penrose, Hawking, and Geroch, all general-relativistic cosmological models must have a singularity. However, the energy condition assumed by the theorems is not satisfied by all known forms of matter. (A notable exception is the massive Klein-Gordon field.) Our object here is to construct exact isotropic cosmological models without singularities by exploiting a violation of the energy condition which arises naturally from the basic physics, rather than being introduced ad hoc via an equation of state. We accomplish this with models in which the matter, envisaged as dust, interacts with a conformal scalar field whose field equation and stress-energy tensor come from an action principle. All the equations that govern the evolution of the models are solved exactly. For all possible topologies of the universe, the singularity can be avoided for a certain range of the parameters of the model, but only for the closed universe is the required range physically appealing.