Quantum of volume in de Sitter space

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.