Predictions and Tests of Multiverse Theories

Abstract

Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it includes suitable measures for observations, what is observable can be explained in terms of the theory even if it contains such unobservable elements. Thus good multiverse theories can be tested against observations. For these tests and Bayesian comparisons of different theories that predict more than one observation, it is useful to define the concept of ``typicality'' as the likelihood given by a theory that a random result of an observation would be at least as extreme as the result of one's actual observation. Some multiverse theories can be regarded as pertaining to a single universe (e.g. a single quantum state obeying certain equations), raising the question of why those equations apply. Other multiverse theories can be regarded as pertaining to no single universe at all. These no longer raise the question of what the equations are for a single universe but rather the question of why the measure for the set of different universes is such as to make our observations not too atypical.

19 pages, LaTeX, version with editorial amendments by Bernard Carr, to appear in B. J. Carr, ed., Universe or Multiverse? (Cambridge University Press, Cambridge, 2007), pp. 401-419