Pre-inflationary scalar perturbations on closed universes in loop quantum cosmology

TL;DR

This paper investigates how pre-inflationary scalar perturbations in a closed universe within loop quantum cosmology affect the primordial power spectrum, revealing potentially observable deviations from standard models due to quantum gravity effects and spatial curvature.

Contribution

It introduces a numerical analysis of scalar perturbations in a closed universe with quantum bounce effects, incorporating pre-inflationary conditions and curvature corrections into the power spectrum.

Findings

Pre-inflationary quantum effects can significantly alter the power spectrum.

Spatial curvature introduces observable corrections to the primordial spectrum.

Deviations from the standard power-law spectrum may be detectable even with small curvature.

Abstract

The inflationary and pre-inflationary evolution of scalar modes of cosmological perturbations in a closed universe is analyzed for a loop quantum cosmology model with an inflationary regime consistent with the constraints on inflation derived from observations of the cosmic microwave background. The effective background dynamics includes a bounce induced by quantum gravity effects. Initial conditions for the perturbations are set before the bounce, and the perturbations are numerically evolved until the end of inflation, allowing the determination of the primordial power spectrum for comoving curvature perturbations. The power spectrum includes corrections due to the presence of spatial curvature and excitations produced before the onset of slow-roll inflation. The deviations from the usual power-law spectrum can be significant for observable modes even for spatial curvatures much smaller than the observational limit obtained without considering the pre-inflationary evolution of the perturbations.