We consider a scalar field with a bottom-less linear potential, finding that cosmologies unavoidably end up with a crunch, even in scenarios compatible with the observed positive cosmological constant. Assuming that rebounces avoid singularities, this generates a new kind of multiverse: the universe undergoes cycles with different cosmological constants, all with finite lifetime regardless of the sign. This novel "temporal" multiverse avoids some of the usual ambiguities present in the standard "spatial" one. Moreover, if a "hiccupping" mechanism changes the vacuum energy by a small amount at each cycle, 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 of 2 orders of magnitude that seems left by standard anthropic selection.