EXTRINSIC TIME IN QUANTUM COSMOLOGY

Extrinsic time is identified in most isotropic and homogeneous cosmolo gical models by matching it with the ideal clock-a parametrized system whose only ''degree of freedom'' is time. Once this matching is estab lished, the cosmological models are quantized in the same way as the i deal clock. The space of solutions of the Wheeler-DeWitt equation is t urned into a Hilbert space by inserting a time-dependent operator in t he inner product, yielding a unitary theory equivalent to the phase-sp ace-reduced theory.