Quantum cosmology and open universes

The quantum creation of universes with compact spacelike sections that have curvature k either closed, flat, or open, i.e., $k=\pm 1,0,$ is studied. In the flat and open cases, the superpotential of the Wheeler-DeWitt equation is significantly modified, and as a result the qualitative behavior of a typical wave function differs from the traditional closed case. In the open case boundary conditions that include the tunneling ones are allowed but not the no-boundary choice. Restricting ourselves to the tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the universe is open, $k=-1.$ In all cases sufficient inflation $\sim 60$ e foldings are predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.