  An extrinsic time is identified in most isotropic and homogeneous
cosmological models by matching them with the ideal clock - a parametrized
system whose only "degree of freedom" is time -. Once this matching is
established, the cosmological models are quantized in the same way as the ideal
clock. The space of solutions of the Wheeler-DeWitt equation is turned out into
a Hilbert space by inserting a time dependent operator in the inner product,
yielding a unitary theory equivalent to the phase space reduced theory.

General Relativity and Quantum Cosmology