Foundational questions in Quantum Cosmology

In this talk, I will introduce one of the first methods for quantising gravity, the Wheeler--DeWitt quantisation, and explain two main foundational issues regarding this approach, the Problem of Time and the Measurement Problem. I will present several proposals for the resolution to these problems using specific cosmological models and I will outline the similarities and differences with Loop Quantum Cosmology. In particular, I will show how singularity resolution is dependent on the way to solve the Problem of Time, and how Spontaneous Collapse Models can make a cosmological model transition form a quantum state to a classical one.