Mode decomposition and unitarity in quantum cosmology

Abstract

Contrary to common belief there are perspectives for generalizing the notion of positive and negative frequency in minisuperspace quantum cosmology, even when the wave equation does not admit symmetries. We outline a strategy for doing so when the potential is positive. An underlying unitarity structure also emerges. Starting from the framework of the Klein-Gordon type quantization, I am led to a result that relies on global features of the model, and that is possibly related to structures encountered in the refined algebraic quantization scheme.