  We explore the extension of quantum cosmology outside the homogeneous
approximation, using the formalism of loop quantum gravity. We introduce a
model where some of the inhomogeneous degrees of freedom are present, providing
a tool for describing general fluctuations of quantum geometry near the initial
singularity. We show that the dynamical structure of the model reduces to that
of loop quantum cosmology in the Born-Oppenheimer approximation. This result
corroborates the assumptions that ground loop cosmology, sheds light on the
physical and mathematical relation between loop cosmology and full loop quantum
gravity, and on the nature of the cosmological approximation. Finally, we show
that the non-graph-changing Hamiltonian constraint considered in the context of
algebraic quantum gravity provides a viable effective dynamics within this
approximation.
