Spacetime Foam and the Cosmological Constant

In the saddle point approximation, the Euclidean path integral for quantum gravity closely resembles a thermodynamic partition function, with the cosmological constant $\Lambda$ playing the role of temperature and the “density of topologies” acting as an effective density of states. For $\Lambda <0\mathrm{}$, the density of topologies grows superexponentially, and the sum over topologies diverges. In thermodynamics, such a divergence 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.