Eternal fractal in the universe
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Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow the 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 of realizing eternal inflation. I show gauge invariance of the condition for the presence of eternal inflation. Finally, I consider the question of whether all thermalized regions merge into one connected domain. The fractal dimension of the eternal set provides a (weak) sufficient condition for merging.
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The ultimate state of the universe is a fractal distribution of inflating and post-inflating regions, in which our local Big Bang is not a particularly unique event.
“the ultimate state of the universe is a fractal distribution of inflating and post-inflating regions [21, 22, 38, 39], in which our local Big Bang is not a particularly unique event.”
From Spontaneous inflation and the origin of the arrow of time (2004) · cites this paper as [39]
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ANNINOS, D. (2012) · International Journal of Modern Physics A · doi:10.1142/s0217751x1230013x · Cited by 174 · see citing works
Spontaneous inflation and the origin of the arrow of time
Carroll, S. M., & Chen, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0410270 · Cited by 135 · see citing works
- Authors
- Winitzki, S.
- Affiliations
- Tufts University (US)
- Corresponding author
- Winitzki, Serge
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2002-03-29
- Volume
- 65
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W1886391637
- Cited by
- 37
- References
- 3
- Citations by year
- 2026: 1 · 2024: 1 · 2021: 1 · 2019: 2 · 2018: 2 · 2016: 4 · 2015: 2 · 2014: 2 · 2012: 2
- FWCI
- 1.24
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- eternal inflation, stochastic inflation, fractal dimension, self-similar spacetimes, gauge invariance, thermalization, large-scale structure
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