Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity

In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S'=\sum_{h \epsilon \{h_1,h_2,...\} } \lambda_h V_h$ 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 $V_{h_1}$, $V_{h_2}$, ... 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.