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A geometrodynamical quantization of an inflationary universe is considered inorder to estimate quantum-gravity effects for the primordial perturbations.Contrary to previous studies in the literature, the back-reaction produced byall the modes of the system is included in our computations. Even if at aclassical level the assumption that every mode evolves independently provides agood estimate for the dynamics, our results explicitly show that this is notthe case when considering quantum-gravity effects. More precisely, both theself-interaction, as well as the back-reaction from other modes, provide acorrection of the same order of magnitude to the usual power spectrum ascomputed in the approximation of quantum field theory on classical backgrounds.In particular, these quantum-gravity effects introduce certain characteristicscale-dependence on the expression of the power spectrum.

Mode coupling on a geometrodynamical quantization of an inflationary universe