Quantization and regularization in perturbative quantum cosmology

Reduction to physical degrees of freedom before quantization leads to predictions for one-loop amplitudes in quantum cosmology in the presence of boundaries which disagree with the results obtained from Faddeev-Popov theory and boundary-counterterms technique. However, the mode-by-mode analysis of eigenvalue equations for gauge modes and ghost fields remains a very difficult problem. Hence, the equivalence or inequivalence of various quantization and regularization techniques cannot be easily proved.