Role of a ''local'' cosmological constant in Euclidean quantum gravity

In 4D nonperturbative Regge calculus a positive Value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form S' = Sigma(h is an element of{h1,h2,...})lambda(h) V-h is added to the gravitational action, where {h(1),h(2),...} is a subset of the hinges and {lambda(h)} are positive constants, one expects that the volumes V-h1, V-h2,... tend to collapse and that the excitations of the lattice propagating through the hinges {h(1),h(2),...} are damped. We study the continuum analogue of this effect. The additional term S' may represent the coupling of the gravitational field to an external Bose condensate.