Loop quantum cosmology of the Bianchi I model: complete quantization
  We complete the canonical quantization of the vacuum Bianchi I model within the improved dynamics scheme of loop quantum cosmology, characterizing the Hilbert structure of the physical states and providing a complete set of observables acting on them. In order to achieve this task, it has been essential to determine the structure of the separable superselection sectors that arise owing to the polymeric quantization, and to prove that the initial value problem obtained when regarding the Hamiltonian constraint as an evolution equation, interpreting the volume as the evolution parameter, is well-posed. 
M Mart\'in-Benito, L J Garay, G A Mena Marug\'an, and E. Wilson-Ewing
gr-qc