Quantum-Mechanical Aspects of Quantum Cosmology

Abstract

In quantum cosmology wave functions are traditionally generated either from path integrals or from solving the Wheeler-DeWitt equation. In the first part of the talk I discuss what is required in these approaches in order to meet the usual requirements of Hilbert space quantum mechanics, namely, the specification of an inner product structure and classes of states and operators of interest. The Wheeler-DeWitt operator must be self-adjoint in this approach which has consequences for the both the path integral and Wheeler-DeWitt account of the much-studied de Sitter minisuperspace model, since it is usually formulated in terms of a scale factor which must be non-negative, hence one is really doing quantum mechanics on the half-line. In the second part of the talk I discuss the types of amplitudes one is interested in from the perspective of the decoherent histories approach to quantum cosmology, which describe whether the trajectory of a cosmological model passes through various regions of minisuperspace. They are different in form to the simplest path integral constructions in quantum cosmology and most closely resemble scattering amplitudes.