Separation distribution of vacuum bubbles in de Sitter space

We compute the probability distribution of the invariant separation between nucleation centers of colliding true vacuum bubbles arising from the decay of a false de Sitter space vacuum. We find that even in the limit of a very small nucleation rate (H-5 much less than 1) the production of widely separated bubble pairs is suppressed. This distribution is of particular relevance for the recently proposed "colliding bubble braneworld" scenario, in which the value Of of (the contribution of negative spatial curvature to the cosmological density parameter) is determined by the invariant separation of the colliding bubble pair. We also consider the probability of a collision with a 'third' bubble. (C) 2002 Elsevier Science B.V. All rights reserved.