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.