Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

is infinite qualitatively different from “really really big?” 185of these measures do correspond to convergent regularizations of sensible-seemingquantities and thus ought to represent something meaningful. Moreover, many of themeasures, while initially seeming distinct, have been shown to be either the same orclosely related; perhaps there are only a small number of reasonable measures. Thestakes are high, as this open question is a major hurdle currently blocking progress inunderstanding the universe on the largest scales, as well as whether string/M theoryand inflation can plausibly reproduce the universe we see.8.5 Is Infinite Qualitatively Different from “Really Really Big?”In the preceding sections, I discussed how everlasting inflation “eventually” brings intobeing an infinite number of bubble universes, each of which is (probably) spatiallyinfinite at each time (according to observers inside it, with their natural time slicing). Inthis section, I would like to discuss the question, “Are there issues in which the infiniteis qualitatively or even observationally different from the finite but extremely large?” Ihave not proven to myself that this is so, but in the following section I discuss severalinstances in which the two cases seem, in some sense, truly different, and in which thedistinction might even have observational import.8.5.1 An Infinitely Old versus an “Almost Infinitely Old” UniverseEverlasting inflation completely alters the classical Big Bang picture of a universespringing into being a finite time ago, because the putative Big Bang (the time at whichthe universe is hot, dense, and homogeneous) results from reheating after an indefinitelylong period of inflation. Indeed, inflation circumvents most of the classic singularitytheorems indicating an initial singularity, because they are based on energy conditionsviolated by a field driving inflation. Nonetheless, it appears to be generally assumed thatwhile inflation continues forever into the future, that it nonetheless started at some fixedtime in a “Big Bang-like” event. But because everlasting inflation approaches a Steady-State mixture of inflating region and bubbles of noninflation, it seems reasonable toask whether inflation might simply be in a steady state, so as to avoid any initial timeor initial singularity and make inflation truly “eternal.”What would this look like? The idea would be to make the state approached byeverlasting inflating into the exact state of the universe at any time Aguirre and Gratton(2002, 2003), Aguirre (2007). The universe would, therefore, be spatially flat (in termsof the inflating background), with a statistical distribution of bubbles that is given bythe distribution of bubbles in everlasting inflation in the t →∞limit.This state has some rather interesting aspects: As described for the Steady-State model, the universe, while expanding and formingmore bubbles, is always the same from one time to another (in the slicing of the inflatingbackground that gives flat spatial sections). There is no sense in which there are morebubbles at one time than at the previous time. Although there is always an inflating region, the fraction of the volume at any time thatis inflating (i.e., the inflating volume divided by the volume that would be inflating if