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 $g \lesssim 1.2 H_0^{2/3} M_{\rm Pl}^{1/3}$. 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.
