Super-inflation in Loop Quantum Cosmology

TL;DR

This paper explores super-inflation dynamics in two Loop Quantum Cosmology models, showing how different quantum corrections influence the power spectrum and solving the horizon problem with minimal e-folds.

Contribution

It compares inverse volume and quadratic quantum corrections in Loop Quantum Cosmology and their effects on super-inflation and the resulting power spectrum.

Findings

Scale invariance achieved for steep negative potentials in the inverse volume case.

Positive potentials approaching a constant yield scale invariance in the quadratic correction case.

Horizon problem solved with only a few e-folds of super-inflation.

Abstract

We investigate the dynamics of super-inflation in two versions of Loop Quantum Cosmology, one in which the Friedmann equation is modified by the presence of inverse volume corrections, and one in which quadratic corrections are important. Computing the tilt of the power spectrum of the perturbed scalar field in terms of fast-roll parameters, we conclude that the first case leads to a power spectrum that is scale invariant for steep power law negative potentials and for the second case, scale invariance is obtained for positive potentials that asymptote to a constant value for large values of the scalar field. It is found that in both cases, the horizon problem is solved with only a few e-folds of super-inflationary evolution.