Robustness of key features of loop quantum cosmology

TL;DR

This paper demonstrates the exact solvability of loop quantum cosmology for the flat FRW model with a scalar field, establishing the generic nature of the quantum bounce, an upper bound on matter density, and clarifying the relation to Wheeler DeWitt theory.

Contribution

It provides an exact analytical analysis of loop quantum cosmology, highlighting the fundamental discreteness and clarifying its differences from Wheeler DeWitt theory.

Findings

Quantum bounce is shown to be generic.

Matter density has a universal upper bound.

Discreteness in LQC is fundamental.

Abstract

Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is shown to be exactly soluble if the scalar field is used as the internal time already in the classical Hamiltonian theory. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.