  In the weak field approximation to quantum gravity, a "local" positive
cosmological term mu^2(x) corresponds to a local negative squared mass term in
the Lagrangian and may thus induce instability and local pinning of the
gravitational field. Such a term can be produced by the coupling to an external
Bose condensate. In the functional integral, the local pinning acts as a
constraint on the field configurations. We discuss this model in detail and
apply it to a phenomenological analysis of recent experimental results.
