Quantum Gravitational Contributions to the CMB Anisotropy Spectrum

TL;DR

This paper derives quantum gravitational corrections to the primordial power spectrum in inflationary cosmology, providing potential observational signatures in the CMB and setting bounds on the inflationary energy scale.

Contribution

It introduces a method to compute quantum gravitational effects on the primordial spectrum using the Wheeler-DeWitt equation and the Born-Oppenheimer approximation.

Findings

Quantum gravitational corrections modify the primordial power spectrum.

Non-observation of corrections constrains the inflationary energy scale.

Recovered scale-invariant spectrum as in standard inflation models.

Abstract

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the CMB anisotropy spectrum. The non-observation so far of such corrections translates into an upper bound on the energy scale of inflation.