Cosmological constant: relaxation vs multiverse

Abstract

We consider a scalar field with a bottom-less potential, such as $g^3\varphi$, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if $g\lesssim 1.2H_0^{2/3}{M}_{\mathrm{Pl}}^{1/3}$. 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.

Comments: 15 pages, 3 figures; published version