CREATION OF UNIVERSES IN SUPERSPACE AND THE PROBLEM OF A NEGATIVE COSMOLOGICAL CONSTANT

The creation of universe containing an amount of matter is studied within a minisuperspace model in the approximation where the back reaction of matter (specifically, the massive scalar field conformally coupled to gravity) on the dynamics of the radius of the universe is neglected. At positive cosmological constant Λ, the number of created universes is exponentially large; it is found that these universes are mostly empty. At negative Λ, the created universes are necessarily filled with matter. We obtain the result that the number of created universes is much larger at large negative Λ than at small positive Λ. This observation makes problematic the attractive proposal for the explanation of the vanishing cosmological constant. The resolution of this difficulty might require invoking anthropic arguments. © 1990.