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 $Λ$ playing the role of temperature and the ``density of topologies'' acting as an effective density of states. For $Λ<0$, 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.

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