On the Topological Phases of Eternal Inflation

Eternal inflation is a term that describes a number of different phenomena which have been classified by Winitzki. According to Winitzki’s classification these phases can be characterized by the topology of the percolating structures in the inflating, “white,” region. In this paper we discuss these phases, the transitions between them, and the way they are seen by a “Census Taker”; a hypothetical observer inside the non-inflating, “black,” region. We discuss three phases that we call, “black island,” “tubular,” and “white island.” The black island phase is familiar, comprised of rare Coleman De Luccia bubble nucleation events. The Census Taker sees an essentially spherical boundary, described by the conformal field theory of the FRW/CFT correspondence. In the tubular phase the Census Taker sees a complicated infinite genus structure composed of arbitrarily long tubes. The white island phase is even more mysterious from the black side. Surprisingly, when viewed from the non-inflating region this phase resembles a closed, positively curved universe which eventually collapses to a singularity. Nevertheless, pockets of eternal inflation continue forever. In addition there is an “aborted” phase in which no eternal inflation takes place. Rigorous results of Chayes, Chayes, Grannan and Swindle establish the existence of all of these phases, separated by first order transitions, in Mandelbrot percolation, a simple model of eternal inflation.