Noether Symmetries in Quantum Cosmology: A Selection Rule for Observable Universes

Noether’s symmetries play a prominent role in any branch of physics. Here, we discuss their role in Quantum Cosmology. In particular, in this Chapter, we consider minisuperspace cosmological models, showing that the existence of symmetries, and then conserved quantities, not only allows to obtain exact cosmological solutions but also gives a selection rule through which one can recover correlations among cosmological parameters, that is a criterion to select observable universes. In this sense, symmetries are related to physically reliable models. Examples are worked out starting from some theories of gravity.