This is an interesting theory for an expanding universe, but it seems to imply that the universe cannot contract: in a contracting universe, the time evolution

This is an interesting theory for an expanding universe, but it seems to imply that the universe cannot contract: in a contracting universe, the time evolution operator would have to be a dimension-reducing isometry, which doesn’t exist. It would certainly be interesting if the true laws of quantum gravity don’t allow contraction regardless of initial conditions.