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Resumo: We investigate the evolution of gauge invariant quantum perturbations in the closed FLRW model in the
presence of an inflationary potential. We first determine initial conditions for the background dynamics which lead to a desired slow-roll phase that is compatible with observations. Providing the initial conditions for the quantized perturbations at the onset of inflation we study the influence of the spatial curvature on the scalar and tensor power spectra at the end of inflation. We determine the implications of the modifications of the primordial power spectra due to the presence of spatial curvature to the CMB spectra and compare our results with the Planck data. We highlight the main differences from the standard inflationary scenario in a flat FLRW model.
