Quantum wavefunctions in expanding spacetimes.

Nowadays, there exists significant observational evidence that our universe is undergoing a period of accelerated expansion. The need for a theoretical framework able to describe the features of such a spacetime at the quantum level then arises naturally. Our aim is precisely to investigate the structure of the quantum Hilbert space of cosmological spacetimes which experience significant time dependence over large scales. In order to study them, we will employ both a Wheeler-DeWitt/wavefunctional perspective, placing particular emphasis on the constraints of the theory, and Euclidean path integral methods. An approach which has often been considered in the literature is examining lower dimensional quantum cosmologies. In fact, these provide an advantageous setting for studying wavefunctions in expanding universes as one has access to a renormalisable theory of gravity and, at the same time, the models retain some features of their higher dimensional counterparts. Interestingly, these quantum gravity models admit a supersymmetric extension and studying it would give us an additional tool to better understand the models themselves. In light of this, it is relevant to explore the broader question of supergravity in a universe undergoing accelerated expansion like de Sitter.