Misc,
Quantum Cosmology
(October 2006)
Abstract
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.
