The Classification of Universes

We define a universe as the contents of a spacetime box with comoving walls, large enough to contain essentially all phenomena that can be conceivably measured. The initial time is taken as the epoch when the lowest CMB modes undergo horizon crossing, and the final time taken when the wavelengths of CMB photons are comparable with the Hubble scale, i.e. with the nominal size of the universe. This allows the definition of a local ensemble of similarly constructed universes, using only modest extrapolations of the observed behavior of the cosmos. We then assume that further out in spacetime, similar universes can be constructed but containing different standard model parameters. Within this multiverse ensemble, it is assumed that the standard model parameters are strongly correlated with size, i.e. with the value of the inverse Hubble parameter at the final time, in a manner as previously suggested. This allows an estimate of the range of sizes which allow life as we know it, and invites a speculation regarding the most natural distribution of sizes. If small sizes are favored, this in turn allows some understanding of the hierarchy problems of particle physics. Subsequent sections of the paper explore other possible implications. In all cases, the approach is as bottoms up and as phenomenological as possible, and suggests that theories of the multiverse so constructed may in fact lay some claim of being scientific.