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

TL;DR

This paper extends the quantum theory of cosmological perturbations into the Planck era using loop quantum gravity, addressing limitations of classical approaches at high densities and curvatures.

Contribution

It introduces a new framework that incorporates quantum gravity effects into cosmological perturbations, clarifying trans-Planckian issues and setting conditions for overcoming them.

Findings

Framework distinguishes true and apparent trans-Planckian problems.

Provides conditions to address quantum gravity effects in early universe.

Lays groundwork for applying to inflationary models in a companion paper.

Abstract

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.