Quantum Cosmology

A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that have the 3-dimensional argument of the wavefunction on their one and only boundary. This proposal is incomplete in several ways but also has had several partial successes, mainly when one takes the zero-loop approximation of summing over a small number of complex extrema of the action. This is illustrated here by the Friedmann-Robertson-Walker-scalar model. In particular, new results are discussed when the scalar field has an exponential potential, which generically leads to an infinite number of complex extrema among which to choose