Lattice Refining Loop Quantum Cosmology from an Isotropic Embedding of Anisotropic Cosmology

We demonstrate that it is possible to produce different isotropic embeddings of anisotropic Loop Quantum Cosmology, resulting to "lattice refinement" in the isotropic system. To introduce the general approach, we first use a simple model with only two anisotropic directions. We then employ the specific case of a Bianchi I model, to show how the method extends to three-dimensional systems. To concisely calculate the step-size of the resulting isotropic state, we define the "symmetric dual" of states and operators, for the two- and three-dimensional systems, respectively.Comment: 19 pages, 1 figure; slightly amended version to appear in Classical and Quantum Gravit