Quantum of volume in de Sitter space

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 $Λ>0$. Modification of the Hamiltonian in terms of loop geometry parametrized by a length $λ$ introduces a scale dependence of the model. The spectrum of the volume operator is discrete and depends on $Λ$. Relating quantum of the volume with an elementary lattice cell leads to an explicit dependence of $Λ$ on $λ$. Based on this assumption, we investigate the possibility of interpreting $Λ$ as a running constant.

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