  This papers offers a critical discussion on the procedure by which Loop
Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG)
theory. Revising recent issues in preserving SU(2) symmetry when quantizing the
isotropic Universe, we trace a new perspective in approaching the cosmological
problem within quantum geometry. The cosmological sector of LQG is reviewed and
a critical point of view on LQC is presented. It is outlined how a polymer-like
scale for quantum cosmology can be predicted from a proper fundamental graph
underlying the homogeneous and isotropic continuous picture. However, such a
minimum scale does not coincide with the choice made in LQC. Finally, the
perspectives towards a consistent cosmological LQG model based on such a graph
structure are discussed.
