Quantum-gravitational corrections to the power spectrum for a closed universe

TL;DR

This paper investigates quantum-gravitational effects on the inflationary power spectrum in a closed universe using canonical quantum gravity and semiclassical approximations, revealing corrections relative to flat models.

Contribution

It introduces a method to compute quantum-gravitational corrections to the power spectrum in a closed universe within the Wheeler-DeWitt framework.

Findings

Quantum-gravitational corrections modify the power spectrum.

Corrections are derived using semiclassical Born-Oppenheimer approximation.

Results are compared to flat universe models.

Abstract

We study the quantum-gravitational corrections to the power spectrum of a gauge-invariant inflationary scalar perturbations in a closed model of a universe. We consider canonical quantum gravity as an approach to quantizing gravity. This leads to the Wheeler-DeWitt equation, which has been studied by applying a semiclassical Born-Oppenheimer type of approximation. At the corresponding orders of approximation, we recover both the uncorrected and quantum-gravitationally corrected Schroedinger equations for the perturbation modes from which we calculate the quantum-gravitational corrections to the power spectrum in the slow-roll regime. The results are compared to the power spectra for the flat model of the universe.