The eternal fractal in the universe
Abstract
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.
Cite
@article{arxiv.gr-qc/0111048,
title = {The eternal fractal in the universe},
author = {Serge Winitzki},
journal= {arXiv preprint arXiv:gr-qc/0111048},
year = {2016}
}
Comments
Conversion to RevTeX4; minor changes; version accepted by Phys. Rev. D