Quantum cosmology, supersymmetry, and the problem of time

Hugh Luckock

( School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia )

Abstract

Quantum cosmology is the application of quantum theory to the Universe as a whole, including the gravitational degrees of freedom. It has been put forward as a way of understanding various features of the Universe (such as its isotropy), and also offers an interesting picture of its origin. However, there remain several fundamental questions about the implementation and interpretation of this approach. In particular, there is much uncertainty about the role of time in quantum cosmology and the interpretation of the wave function of the Universe. Recent work has raised hopes that supersymmetry might shed light on these questions. Indeed, supersymmetry simplifies the mathematical structure of the quantum theory and suggests entirely new approaches to some of the most important outstanding issues.

There follows a brief review of the ideas underlying quantum cosmology, and of the role which might be played by supersymmetry. There is also a short summary of work done recently with Robert Graham on the emergence of a cosmological time parameter in quantum supergravity, which provides a possible solution to the ``Problem of Time''.