Convergence of Perturbations for a Big Bounce in Loop Quantum Cosmology

TL;DR

This paper studies the behavior of scalar and vector perturbations during a big bounce in loop quantum cosmology, showing that certain perturbations remain well-behaved and that the bounce is physically plausible.

Contribution

It demonstrates the convergence of perturbations in two loop quantum cosmology models and shows the avoidance of unbounded vector growth, supporting the physical viability of the bounce.

Findings

Scalar perturbations behave well near the bounce and transition points.

Vector perturbations avoid unlimited growth in the model.

Maximum vector mode amplitude inversely proportional to the square of the minimum scale factor.

Abstract

We investigate the convergence behaviors of the scalar and the vector perturbations for a big bounce phase in loop quantum cosmology. Two models are discussed: one is the universe filled by a massless scalar field; the other is a toy model which is radiation-dominated in the asymptotic past and future. We find that the behaviors of the Bardeen potential of the scalar mode near both the bounce point and the transition point of the null energy condition are good, moreover, the unlimited growth of the vector perturbation can be avoided in our bounce model. This is different from the bounce models in pure general relativity. And we also find that the maximum of an observable vector mode is inversely proportional to the square of the minimum scalar factor $a_{bounce}$. This conclusion is independent with the bounce model, and we may conclude that the bounce in loop quantum cosmology is reasonable.