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

An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era