Quantum Cosmology

Summary

INTRODUCTION

The presumed breakdown of the general theory of relativity (GTR) at the Planck scale without, as yet, a complete quantum theory of gravity (QG) to replace it is used to motivate consideration of a simpler problem—the quantum mechanics of cosmological models. In a pioneering paper, Misner (1969a) coined the term “quantum cosmology” (QC) for the quantization of the dynamical system whose degrees of freedom describe a spatially homogeneous universe. He also introduced the term “minisuperspace” (MSS) (Misner 1972) for the finite-dimensional configuration space of the dynamics of homogeneous cosmologies—a finite subspace of Wheeler's “superspace” (Wheeler 1968), the space of all three-geometries. The first invocation of quantized MSS models was that of DeWitt (1967) to apply Dirac (1958, 1959) quantization of gravity to a tractable system. He considered the closed Friedmann-Robertson-Walker (FRW) model (see Misner et al 1973). Misner (1969a, 1970, 1972) considered the application of Arnowitt, Deser, and Misner (1962) (ADM) quantization methods to the Bianchi Type cosmologies (e.g. Ryan and Shepley 1975, MacCallum 1975). In both treatments, it became clear that issues of time, factor ordering, and interpretation which plague the canonical quantization of gravity survive in the truncated models. It was, of course, recognized that, while perfectly valid as classical solutions to Einstein's equations, quantized cosmologies where degrees of freedom have been zeroed by hand need have no relation to a true QG theory. [A systematic attack on the validity of the MSS “approximation” has only recently begun (Kuchař and Ryan 1986, 1989).] Misner argued (1969a) that one might reasonably expect the quantum universe to be dominated by the dynamics of its spatially homogeneous mode.