The Definition and Classification of Universes ∗

We assume that the concept of a multiverse makes sense, and suggest a specific, standardized definition for member universes which are similar to our own. Central to this description is the definition of size, which is taken to be the asymptotic value, at large times, of the inverse Hubble constant. Thus the cosmological constant plays a central role in defining the properties of the subset of universes similar to our own. We then assume that vacuum parameters and coupling constants of the standard model are dependent upon the size of a universe, and propose a specific form for the dependence. Anthropic considerations then limit the size of habitable universes (as we understand that concept) to be within a factor two of our own. Implications of this picture for understanding the standard-model “hierarchy problem” are discussed, as are general issues of falsifiability and/or verifiability of these ideas. Contribution to the proceedings of the symposium “Universe or Multiverse?” Sponsored by the John Templeton Foundation Stanford University, Stanford, California March 2003 ∗Work supported by Department of Energy contract DE–AC02–76SF00515. 1,