  In a recent proposal using the group field theory approach, a spatially
homogeneous (generally anisotropic) universe is described as a quantum gravity
condensate of "atoms of space," which allows the derivation of an effective
cosmological Friedmann equation from the microscopic quantum gravity dynamics.
Here we take a first step towards the study of cosmological perturbations over
the homogeneous background. We consider a state in which a single "atom" is
added to an otherwise homogeneous condensate. Backreaction of the perturbation
on the background is negligible and the background dynamics can be solved
separately. The dynamics for the perturbation takes the form of a quantum
cosmology Hamiltonian for a "wave function," depending on background and
perturbations, of the product form usually assumed in a Born-Oppenheimer
approximation. We show that the perturbation we consider corresponds to a
spatially homogeneous metric perturbation, and for this case derive the usual
procedures in quantum cosmology from fundamental quantum gravity.
