The Semiclassical Limit of Loop Quantum Cosmology

TL;DR

This paper explores how loop quantum cosmology approaches the classical continuum limit, emphasizing the role of the Barbero-Immirzi parameter and connecting it to standard quantum cosmology.

Contribution

It demonstrates that standard quantum cosmology emerges as a simultaneous limit of loop quantum cosmology when the Barbero-Immirzi parameter goes to zero and volume labels go to infinity.

Findings

Standard quantum cosmology is the limit of loop quantum cosmology as   0, j  .

The limit \u0010  0, j   is analogous to the classical limit in quantum mechanics.

Insights into semiclassical states in the full quantum geometry theory are discussed.

Abstract

The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit \gamma \to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultaneous limit is technically the same as the classical limit \hbar \to 0, l \to \infty of angular momentum in quantum mechanics. Possible lessons for semiclassical states at the dynamical level in the full theory of quantum geometry are mentioned.