  In this companion to our letter (arXiv:2208.10514), we elaborate the full
details of the predicted corrections to the primordial scalar and tensor power
spectra that arise from quantum gravity-motivated, natural, covariant
ultraviolet cutoffs. We implement these cutoffs by covariantly restricting the
fields which are summed over in the path integrals for the primordial
correlators, and we discuss in detail the functional analytic techniques
necessary for evaluating such path integrals. Our prediction, which is given in
terms of measured cosmological parameters and without assuming any particular
inflationary potential, is that the corrections take the form of small
oscillations which are superimposed on the conventional power spectra. The
frequency of these oscillations only depends on the location of the cutoff
scale and the first inflationary slow-roll parameter, while the amplitude and
phase are also moderately sensitive to how smoothly the cutoff turns on. The
specificity of the new predictions offers an opportunity to significantly
enhance experimental sensitivity in observations of the cosmic microwave
background and large-scale structure. This may be used to place ever higher
bounds on the scale at which quantum gravity effects become important in
quantum field theory or may even provide positive evidence for quantum gravity
effects.
