The eternal fractal in the universe
Abstract
Models of eternal inflation predict a stochastic selfsimilar 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 coordinateindependent 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:grqc/0111048
 Bibcode:
 2001gr.qc....11048W
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
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