Loop quantum cosmology of k=1 FRW: A tale of two bounces

TL;DR

This paper investigates two different quantization methods in loop quantum cosmology for the closed k=1 FRW model, revealing that one method predicts a cyclic universe with two distinct bounces, unlike the single bounce in the standard approach.

Contribution

It compares two quantization approaches in loop quantum cosmology for the k=1 FRW model, highlighting the existence of two bounces in the new method.

Findings

The new quantization method predicts two bounces in the cyclic universe.

For large universes, the two bounces are nearly indistinguishable from the standard theory.

The two quantizations coincide in flat and anisotropic models, but differ in the closed k=1 case.

Abstract

We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially non-flat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed $k$=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a `large' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the holonomy based quantum theory.