Anti-deSitter universe dynamics in LQC

TL;DR

This paper explores the dynamics of a flat isotropic universe with a negative cosmological constant in Loop Quantum Cosmology, showing quantum effects replace singularities with bounces, leading to cyclic evolution.

Contribution

It extends Loop Quantum Cosmology methods to a universe with negative cosmological constant, constructing the physical Hilbert space and Dirac observables for this model.

Findings

Quantum dynamics match classical behavior at low energies.

Singularities are replaced by quantum bounces.

Universe exhibits cyclic evolution due to quantum effects.

Abstract

A model for a flat isotropic universe with a negative cosmological constant $\Lambda$ and a massless scalar field as sole matter content is studied within the framework of Loop Quantum Cosmology. By application of the methods introduced for the model with $\Lambda=0$, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the $k=1$ FRW model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in Loop Quantum Cosmology the evolution is qualitatively cyclic.