Wormholes and the cosmological constant

We review Coleman's wormhole mechanism for the vanishing of the cosmological constant. We show that in a minisuperspace model wormhole-connected universes dominate the path integral. We also provide evidence that the euclidean path integral over geometries with spherical topology is unstable with respect to formation of infinitely many wormhole-connected 4-spheres. Consistency is restored by summing over all topologies, which leads to Coleman's result. Coleman's argument for determination of other parameters is reviewed and applied to the mass of the pion. A discouraging result is found that the pion mass is driven to zero. We also consider qualitatively the implications of the wormhole theory for cosmology. We argue that a small number of universes containing matter and energy may exist in contact with infinitely many cold and empty universe. Contact with the cold universe insures that the cosmological constant in the warm ones in zero.