On the uniqueness of kinematics of loop quantum cosmology

The holonomy-flux algebra A of loop quantum gravity is known to admit a natural representation that is uniquely singled out by the requirement of covariance under spatial diffeomorphisms. In the cosmological context, the requirement of spatial homogeneity naturally reduces A to a much smaller algebra,ARed, used in loop quantum cosmology. In Bianchi Imodels, it is shown that the requirement of covariance under residual diffeomorphism symmetries again uniquely selects the representation of ARed that has been commonly used. We discuss the close parallel between the two uniqueness results and also point out a difference.