  Cosmological perturbations are generally described by quantum fields on
(curved but) classical space-times. While this strategy has a large domain of
validity, it can not be justified in the quantum gravity era where curvature
and matter densities are of Planck scale. Using techniques from loop quantum
gravity, the standard theory of cosmological perturbations is extended to
overcome this limitation. The new framework sharpens conceptual issues by
distinguishing between the true and apparent trans-Planckian difficulties and
provides sufficient conditions under which the true difficulties can be
overcome within a quantum gravity theory. In a companion paper, this framework
is applied to the standard inflationary model, with interesting implications to
theory as well as observations.
