Is minisuperspace quantization valid?: Taub in mixmaster

The paper addresses quantitatively the question of the validity of physical predictions based on minisuperspace quantization of Einstein's theory of gravitation. It studies a homogeneous, anisotropic cosmological model of higher symmetry (the Taub model) embedded in one of lesser symmetry (the mixmaster model). The comparison of the physical behavior of these two models is based on the construction of a non-negative probability density and the associated conserved inner product which allow a consistent probabilistic interpretation of the state function of the Universe in the interesting regime of deep channel penetration. It is shown that the respective behavior is widely different. A program is set for investigating a hierarchy of models with higher symmetry embedded in models of lesser symmetry to spell out the criteria under which minisuperspace quantum results can be expected to make meaningful predictions about full quantum gravity.