SPACETIME FOAM AND THE COSMOLOGICAL CONSTANT

In the saddle point approximation, the Euclidean path integral for qua ntum gravity closely resembles a thermodynamic partition function, wit h the cosmological constant Lambda playing the role of temperature and the ''density of topologies'' acting as an effective density of state s. For Lambda < 0, the density of topologies grows superexponentially, and the sum over topologies diverges. In thermodynamics, such a diver gence can signal the existence of a maximum temperature. The same may be true in quantum gravity: the effective cosmological constant may be driven to zero by a rapid rise in the density of topologies.