QUANTUM COSMOLOGY WITH CONFORMALLY INVARIANT SCALAR FIELD

A Friedmann-Robertson-Walker universe filled with a conformally invari ant scalar field is quantized by the reduced phase space method. In th e gauge t = R, where R is the scale factor, a complete set of quantum states is exhibited, whose properties are compared to those of the Har tle-Hawking and Vilenkin wave functions. The issue of time, singularit ies, and shortcomings of the current theories of initial conditions ar e discussed.