  In loop quantum gravity, states of the gravitational field turn out to be
excitations over a vacuum state that is sharply peaked on a degenerate spatial
geometry. While this vacuum is singled out as fundamental due to its invariance
properties, it is also important to consider states that describe
non-degenerate geometries. Such states have features of Bose condensate ground
states. We discuss their construction for the Lie algebra as well as the Weyl
algebra setting, and point out possible applications in effective field theory,
Loop Quantum Cosmology, as well as further generalizations.
