  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 paper,
we will show how quantum states describing a spatially flat homogeneous and
isotropic universe can be refined and coarse grained. Invariance of the
dynamics of the coarse observables is shown to require a certain scaling
property (familiar from loop quantum cosmology) of the quantum states if no
running of parameters is taken into account. 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.
