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.

6 pages, 3 figures, version accepted for publication in Phys. Rev. D

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