Bridging between descriptions involving few large and many small quantum numbers is

the main open problem in loop quantum gravity. In other words, one would like to be

able to represent the same physical system in terms of a few “coarse” quantum

numbers, while the effective dynamics at the coarse level should agree with the one

induced by a description involving many small quantum numbers. Efforts to understand

this relationship face the problem of the enormous computational complexity involved

in evolving a generic state containing many quanta. In a cosmological context

however, certain symmetry assumptions on the quantum states allow to simplify the

problem. In this talk, we will discuss how quantum states describing a spatially

flat homogeneous and isotropic universe can be refined while the dynamics of the

coarse observables is unchanged. The involved states are solutions to the

Hamiltonian constraint when terms coming from spatial derivatives are neglected,

i.e. one works in the approximation of non-interacting FRW patches. The technical

means to arrive at this result are a version of loop quantum gravity based on

variables inspired by loop quantum cosmology, as well as an exact solution to the

quantum dynamics of loop quantum cosmology which extends to the full theory in the

chosen approximation.