Large-scale-small-scale duality and the cosmological constant

We study a model of quantum cosmology originating from a classical model of gravitation where a self-interacting scalar field is coupled to gravity wi th the metric undergoing a signature transition. We show that there are dua l classical signature changing solutions, one at large scales and the other at small scales. It is possible to fine-tune the physics in both scales wi th an infinitesimal effective cosmological constant. (C) 1999 Published by Elsevier Science B.V. All rights reserved.