  We consider quantization of the positive curvature Friedmann cosmology in the
unimodular modification of Einstein's theory, in which the spacetime
four-volume appears as an explicit time variable. The Hamiltonian admits
self-adjoint extensions that give unitary evolution in the Hilbert space
associated with the Schr\"odinger equation. The semiclassical estimate to the
no-boundary wave function of Hartle and Hawking is found. If this estimate is
accurate, there is a continuous flux of probability into the configuration
space from vanishing three-volume, and the no-boundary wave function evolves
nonunitarily. Generalizations of these results hold in a class of anisotropic
cosmologies. (Talk given at the 5th Canadian Conference on General Relativity
and Relativistic Astrophysics, Waterloo, Ontario, Canada, May 1993.)
