“Eternal inflation” is a term that describes a number of different phenomena that 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 noninflating, “black,” region. We discuss three phases that we call “black island,” “tubular,” and “white island.” The black island phase is familiar, composed of rare Coleman De Luccia bubble nucleation events. The Census Taker sees an essentially spherical boundary, described by the conformal field theory of the Friedmann-Robertson-Walker/conformal field theory (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 noninflating region this phase resembles a closed, positively curved universe that 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.

• Received 8 April 2010

DOI:https://doi.org/10.1103/PhysRevD.81.123515