On the Semiclassical Limit of Loop Quantum Cosmology

TL;DR

This paper investigates the semiclassical behavior of a solvable loop quantum cosmology model, analyzing coherent and squeezed states, and demonstrates the preservation of semiclassicality across the quantum bounce.

Contribution

It provides an analytical framework for understanding semiclassical limits in loop quantum cosmology using Gaussian and squeezed states, including criteria for semiclassicality and effects of topology.

Findings

Semiclassicality is preserved across the bounce for all considered states.

Analytical Gaussian coherent states effectively describe the semiclassical regime.

Topology influences the recovery of classical scaling symmetry.

Abstract

We consider a k=0 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state solutions for each point on the space of classical states. We propose physical criteria that select from these coherent states, those that display semiclassical behavior, and study their properties in the deep Planck regime. Furthermore, we consider generalized squeezed states and compare them to the Gaussian states. The issue of semiclassicality preservation across the bounce is studied and shown to be generic for all the states considered. Finally, we comment on some implications these results have, depending on the topology of the spatial slice. In particular we consider the issue of the recovery, within our class of states, of a scaling symmetry present in the classical description of the system when the spatial topology is non-compact.