  We explore the symmetry reduced form of a non-perturbative solution to the
constraints of quantum gravity corresponding to quantum de Sitter space. The
system has a remarkably precise analogy with the non-relativistic formulation
of a particle falling in a constant gravitational field that we exploit in our
anaylsis. We find that the solution reduces to de Sitter space in the
semi-classical limit, but the uniquely quantum features of the solution have
peculiar property. Namely, the unambiguous quantum structures are neither of
Planck scale nor of cosmological scale. Instead, we find a periodicity in the
volume of the universe whose period, using the observed value of the
cosmological constant, is on the order of the volume of the proton.
