Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-11-15
Phys.Rev. D65 (2002) 083506
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Conversion to RevTeX4; minor changes; version accepted by Phys. Rev. D
Scientific paper
10.1103/PhysRevD.65.083506
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.
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