Avoidance of Classical Singularities in Quantized Gravitational Dust Systems

We use the canonical quantization of spherically symmetric dust universes, and calculate the expectation values of the quantized metric, < Ψ|ĝμν |Ψ >. Though the classical solutions are singular, and the wave functions have no zero support on singular geometries, the expectation value (for a general quantum state) is everywhere regular. For a quasi-classical (coherent) state, |α >, the expectation value, < α|ĝ|α > describes a universe (or star) that collapses to a minimum radius, the Planck radius, and re-expands again. This work is supported by the NSF grant PHY 93-15811