The wave function of the universe

Solomons, Deon Mark

The wave function of the universe

Master Thesis

1994

Publisher

University of Cape Town

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

In Quantum Cosmology, universe states are treated as wave function solutions to a zero-energy Schroedinger equation that is hyperbolic in its second derivatives of spatial geometries and matter-fields. In order to select one wave function (that would in principle correspond to our Universe) out of infinitely many, requires an appropriate boundary condition. The Hartle-Hawking No Boundary and the Vilenkin Tunneling proposals are examples of such boundary conditions. We review their applications and shortcomings in the context of the Inflationary Scenario. Another boundary condition is that of S.W. Hawing and D.N. Page (1990) in the context of wormholes. Wormholes are generally considered to play a major role in setting the cosmological constant to zero and to provide a mechanism for black hole evaporation. It is significant that we are able to show that even the class of bulk matter wormhole instantons found by Carlini and Mijic (1990) are predicted in the quantum theory. However, unresolved issues and newfound problems seem to threaten the wormhole theory. Furthermore, since there are no a priori notions of time (and space) present in the quantum theory, it is important to show exactly how the notion of time is recovered over distances much larger than the Planck scale. A good notion of time is also essential for any quantum theory to predict the correct classical behaviour for the Universe today. The issue of time inevitably re-emerges throughout our work.