Quantum of volume in de Sitter space

TL;DR

This paper explores the quantization of a flat cosmological model with a scalar field and positive cosmological constant using loop quantum cosmology, revealing a discrete volume spectrum and proposing a link between the cosmological constant and quantum geometry scale.

Contribution

It introduces a scale-dependent Hamiltonian in loop quantum cosmology and investigates the potential interpretation of the cosmological constant as a running parameter.

Findings

The volume operator spectrum is discrete and depends on $\Lambda$.

A relationship between the quantum of volume and the lattice cell size is established.

The possibility of interpreting $\Lambda$ as a running constant is discussed.

Abstract

We apply the nonstandard loop quantum cosmology method to quantize a flat Friedmann-Robertson-Walker cosmological model with a free scalar field and the cosmological constant $\Lambda>0$. Modification of the Hamiltonian in terms of loop geometry parametrized by a length $\lambda$ introduces a scale dependence of the model. The spectrum of the volume operator is discrete and depends on $\Lambda$. Relating quantum of the volume with an elementary lattice cell leads to an explicit dependence of $\Lambda$ on $\lambda$. Based on this assumption, we investigate the possibility of interpreting $\Lambda$ as a running constant.