The problem of time of quantum gravity has been argued to make canonical approaches unsatisfactory. In this article I study how it affects quantum cosmology and reach the same conclusion. The advantage of studying the cosmological case is that its simplicity makes the discussion much clearer and less technical. The classical models I will be concerned with describe how two degrees of freedom, the scale factor and a scalar field, evolve with respect to a time variable. After quantizing the model, this time variable just disappears, and I argue that this is problematic. Indeed, this variable in the classical model allowed us to make claims like ‘the universe is 13.8 billion years old’ and I will argue that these claims are physically meaningful predictions that are lost in quantum cosmology. I will analyze some of the relational positions in the quantum gravity and quantum cosmology literature that tend to deny the physical meaning of time variables and I will argue against them for the case of classical cosmology. I conclude that the age of the universe is a physical prediction of classical cosmological models, that it is missing from quantum cosmology, and that this should make us suspect that there is something wrong with this sort of approach.
Álvaro Mozota Frauca (Tue,) studied this question.