Classical and Quantum Dynamics of a Closed Universe

Abstract

This report will attempt to describe briefly a new technique in cosmological theory, and some applications, interpretations, and conjectures that can utilize it. The technique is the use of the Arnowitt, Deser, and Misner^l (ADM) Hamiltonian methods for formulating and solving the Einstein equations for homogeneous cosmological models.² Among the applications are a simplified and more detailed presentation³ of the Mix-Master Universe.⁴ This is a closed universe in which it is possible⁵ for light rays to travel completely around the universe in certain epochs near the initial singularity. Some numerical examples of the evolution of these models have been given by Okerson.⁶ As another application, these techniques have allowed Ryan⁷’⁸ to give a concise description of a closed expanding universe model which has rotation as well as shear, but does not employ a cosmological constant. This Hamiltonian technique also leads to models of quantized geometry² which should be useful as a testing ground for many ideas concerning the full quantum theory of curved space-time. The main application developed so far is a study of quantum effects on the initial singularity in closed universes which I have pursued in collaboration with Dr. Kenneth Jacobs and Professor Harold Zapolsky.⁹

Supported in part by NSF Grant GP8560 and NASA Grant NSG-21-002-010.

Invited talk given June 3, 1969, at the. Relativity Conference in the Midwest, Cincinnati, Ohio.