Inflation aside, there might be other mechanisms that create universes. An idea proposed by Richard Tolman and John Wheeler and recently elaborated on by Paul Steinhardt and Neil Turok is that our cosmic history is cyclic, going through an infinite series of Big Bangs. If it exists, the ensemble of such incarnations would also form a multiverse, perhaps with a diversity similar to that of Level II. However, the cyclic models are ruled out by the gravitational wave observations of BICEP2.
