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 playing the role of temperature and the "density of topologies" acting as an effective density of states. For ! 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. PACS numbers: 04.60.Gw, 98.80.Hw email: carlip@dirac.ucdavis.edu The cosmological constant ---in modern language, the energy density of the vacuum---is observed to be less than 10 \Gamma47 GeV 4 , or 10 \Gamma120 in Planck units. The cosmological constant problem [1, 2], the problem of explaining the smallness of this number, is one of the central puzzles of modern physics. A natu..