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Spontaneous decompactification
Open accessAbstract
Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher-dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology.
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The tunneling results in the formation of an expanding bubble, inside of which the compact sphere is destabilized and its radius grows with time.
“The tunneling results in the formation of an expanding bubble, inside of which the compact sphere is destabilized and its radius grows with time.”
From Transdimensional tunneling in the multiverse (2010) · cites this paper as [6]
The Overview (section 5) says tunneling forms an expanding bubble, and the Figure 3 caption describes extra dimensions expanding inside it. Section 2.1 models the changing size of a compact internal space, but the paper does not specify that this space is a sphere. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe radius of the compact dimensions in 6d Einstein-Maxwell theory compactified on a sphere is stabilized by a magnetic flux through the sphere, but the resulting vacua are only metastable and can decay by quantum tunneling through a barrier.
“The radius of the compact dimensions in this theory is stabilized by a magnetic flux through the sphere, but the resulting vacua are only metastable and can decay by quantum tunneling through a barrier.”
From Transdimensional tunneling in the multiverse (2010) · cites this paper as [6]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredAt late times t→∞, the 6d metric in the bubble interior approaches that of dS6, with a(t)≈H6^-1 sinh(H6 t) and r(t)≈H6^-1 cosh(H6 t).
“At late times, t → ∞, the metric approaches that of dS 6 [6], with a(t) ≈ H -1 6 sinh(H 6 t) and r(t) ≈ H -1 6 cosh(H 6 t).”
From Transdimensional tunneling in the multiverse (2010) · cites this paper as [6]
Section 4.2 (eq. 4.16; page unavailable) says that, in the special case of a positive higher-dimensional cosmological constant, the asymptotic metric locally resembles de Sitter space. The later discussion says it asymptotes to (d+4)-dimensional de Sitter space, which includes six dimensions when d=2. Our copy does not give the claimed sinh and cosh formulas for a(t) and r(t). (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe number of large spatial dimensions may vary from vacuum to vacuum, as expected in string theory.
“Yet the number of large spatial dimensions may vary from vacuum to vacuum [9,10,11,12], as is expected in string theory.”
From Observable effects of anisotropic bubble nucleation (2010) · cites this paper as [9]
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Citations
Cites
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Cited by
Sorted by citations
Observable effects of anisotropic bubble nucleation
Blanco-Pillado, J. J., & Salem, M. P. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/07/007 · Cited by 44
Transdimensional tunneling in the multiverse
Blanco-Pillado, J. J., Schwartz-Perlov, D., & Vilenkin, A. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/05/005 · Cited by 38
Paul, A., & Paban, S. (2026) · Journal of High Energy Physics · doi:10.1007/jhep09(2026)188
Metadata
- Authors
- Giddings, S. B., & Myers, R. C.
- Affiliations
- University of California, Santa Barbara (US)
- University of Waterloo (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2004-08-25
- Volume
- 70
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W3037609443
- Cited by
- 59
- References
- 6
- Citations by year
- 2026: 3 · 2024: 1 · 2023: 1 · 2022: 1 · 2021: 2 · 2019: 1 · 2017: 2 · 2015: 2 · 2012: 3
- FWCI
- 3.93
- 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) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy (FG02-91ER40618, 91ER40618)
- Institut Périmètre de physique théorique
- Natural Sciences and Engineering Research Council of Canada
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- extra dimensions, quantum tunneling, thermal fluctuations, higher-dimensional cosmology, fixed-point solutions, spatial curvature
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