A simple model of a Friedmann universe filled with a quantised scalar field

Abstract

IT is widely felt that the ultimate resolution of the problem of gravitational collapse awaits the formulation of a good theory of quantum gravity. Recently, however, it has been suggested (L. Parker and S. A. Fulling, unpublished) that singularities may be avoided because of quantum effects of the matter distribution rather than those of the gravitational field. When the radius of curvature of space–time becomes of the order of, say, 10⁻¹³ cm one expects that the matter distribution might be more appropriately described by a quantum field than by its traditional description as a classical fluid. Since a quantum field need not necessarily respect the energy conditions required by the Hawking–Penrose singularity theorems, there exists, at least in principle, the possibility that in a gravitational collapse the radius of curvature of space–time may always remain much greater than the Planck length (10⁻³³ cm) at which quantum gravitational effects are expected to become important.