%0 Journal Article
%T The eternal fractal in the universe
%A Serge Winitzki
%J Physics
%D 2001
%I arXiv
%R 10.1103/PhysRevD.65.083506
%X Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the ``eternal fractal''). I also derive a nonlinear branching diffusion equation describing global properties of the eternal set and the probability to realize eternal inflation. I show gauge invariance of the condition for presence of eternal inflation. Finally, I consider the question of whether all thermalized regions merge into one connected domain. Fractal dimension of the eternal set provides a (weak) sufficient condition for merging.
%U http://arxiv.org/abs/gr-qc/0111048v2