Cosmological constant: Relaxation vs multiverse

We consider a scalar field with a bottom-less potential, such as g(3)phi, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if g less than or similar to 1.2H(0)(2/3)M(Pl)(1/3). If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that seems left by standard anthropic selection. (C) 2019 The Author(s). Published by Elsevier B.V.