  A geometrodynamical quantization of an inflationary universe is considered in
order to estimate quantum-gravity effects for the primordial perturbations.
Contrary to previous studies in the literature, the back-reaction produced by
all the modes of the system is included in our computations. Even if at a
classical level the assumption that every mode evolves independently provides a
good estimate for the dynamics, our results explicitly show that this is not
the case when considering quantum-gravity effects. More precisely, both the
self-interaction, as well as the back-reaction from other modes, provide a
correction of the same order of magnitude to the usual power spectrum as
computed in the approximation of quantum field theory on classical backgrounds.
In particular, these quantum-gravity effects introduce certain characteristic
scale-dependence on the expression of the power spectrum.
