（ABSTRACT）

We study various phases of eternal inflation. We assume there is an inflating false vacuum which decays to a non-inflating true vacuum by bubble nucleation.
The phases are characterized by the topology of percolating structures at future infinity. We show the existence of three phases by using results on Mandelbrot's fractal percolation model, and study the spacetime geometry in each phase. In the "black island" phase, non-inflating regions form isolated islands. This can be understood as small deformation of the Coleman-De Luccia bubble. In the "tubular" phase, both regions percolate, and the Census Taker (time-like observer in the true vacuum) sees a complicated infinite genus structure composed of arbitrarily long tubes.
In the "white island" phase, the inflating regions are isolated islands.
From the Census Taker's point of view, all but one inflating regions are behind black hole horizon. We argue that this universe eventually collapses.

Reference:
Y. Sekino, S. Shenker and L. Susskind, Phys. Rev. D81 (2010) 123515, arXiv:1003.1347 [hep-th].