  We introduce a class of states characterized by proposed conditions of
homogeneity and isotropy in loop quantum gravity and construct concrete
examples given by Bell-network states on a special class of homogeneous graphs.
Such states provide new representations of cosmological spaces that can be
explored for the formulation of cosmological models in the context of loop
quantum gravity. We show that their local geometry is described in an
automorphism-invariant manner by one-node observables analogous to the one-body
observables used in many-body quantum mechanics, and compute the density matrix
representing the restriction of global states to the algebra of one-node
observables. The von Neumann entropy of this density matrix provides a notion
of entanglement entropy of a local region which respects
automorphism-invariance and can be applied to states involving superpositions
of distinct graphs.
