Anti-deSitter universe dynamics in LQC

Understand

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.