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Mode coupling on a geometrodynamical quantization of an inflationary universe

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.