RADIATION-DOMINATED QUANTUM FRIEDMANN MODELS

Radiation-filled Friedmann-Robertson-Walker universes are quantized ac cording to the Amowitt-Deser-Misner formalism in the conformal-time ga uge. Unlike previous treatments of this problem, here both closed and open models are studied, only square-integrable wave functions are all owed, and the boundary conditions to ensure self-adjointness of the Ha miltonian operator are consistent with the space of admissible wave fu nctions. It turns out that the tunneling boundary condition on the uni versal wave function is in conflict with self-adjointness of the Hamil tonian. The evolution of wave packets obeying different boundary condi tions is studied, and it is generally proven that all models are nonsi ngular. Given an initial condition on the probability density under wh ich the classical regime prevails, it is found that a closed universe is certain to have an infinite radius, a density parameter Omega=1 bec oming a prediction of the theory. Quantum stationary geometries are sh own to exist for the closed universe model, but oscillating coherent s tates are forbidden by the boundary conditions that enforce self-adjoi ntness of the Hamiltonian operator. (C) 1996 American Institute of Phy sics.