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We compute the corrections to the primordial power spectrum that should arise in realistic inflationary scenarios if there exists a generic covariant ultraviolet (UV) cutoff, as commonly motivated by considerations of quantum gravity. The corrections to the spectrum consist of small superimposed oscillations whose frequency, phase, and amplitude are functions of the comoving wave number. For any given cosmological parameters that characterize the slow roll during inflation, the frequency predicted for these oscillations depends only on the value of the UV cutoff. The specificity of this prediction can be used to increase experimental sensitivity through the filtering for template signatures. This will allow experiments to put new bounds on where a natural UV cutoff can be located between the Planck scale and the Hubble scale during inflation. It may even bring imprints of Planck-scale physics in the cosmic microwave background and in structure formation within the range of observations.