A unified perspective on uniqueness criteria for the quantization of cosmological systems

A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

A brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems is provided.These criteria impose some conditions on the representation of a group of physically relevant linear transformations that may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction, or with dynamical transformations that in fact are not symmetries.We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization, a demand that can be seen as a weaker version of the requirement of invariance.