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Cited by 39Black Holes and Theoretical PhysicsCosmology and Gravitation TheoriesNoncommutative and Quantum Gravity Theories

Hyperbolic compactification of M-theory and de Sitter quantum gravity

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De Luca, Giuseppe Bruno, Silverstein, Eva, Torroba, Gonzalo·2022·SciPost Physics
DOI 10.21468/scipostphys.12.3.083
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Abstract

We present a mechanism for accelerated expansion of the universe in the generic case of negative-curvature compactifications of M-theory, with minimal ingredients. M-theory on a hyperbolic manifold with small closed geodesics supporting Casimir energy -- along with a single classical source (7-form flux) -- contains an immediate 3-term structure for volume stabilization at positive potential energy. Hyperbolic manifolds are well-studied mathematically, with an important rigidity property at fixed volume. They and their Dehn fillings to more general Einstein spaces exhibit explicit discrete parameters that yield small closed geodesics supporting Casimir energy. The off-shell effective potential derived by M. Douglas incorporates the warped product structure via the constraints of general relativity, screening negative energy. Analyzing the fields sourced by the localized Casimir energy and the available discrete choices of manifolds and fluxes, we find a regime where the net curvature, Casimir energy, and flux compete at large radius and stabilize the volume. Further metric and form field deformations are highly constrained by hyperbolic rigidity and warping effects, leading to calculations giving strong indications of a positive Hessian, and residual tadpoles are small. We test this via explicit back reacted solutions and perturbations in patches including the Dehn filling regions, initiate a neural network study of further aspects of the internal fields, and derive a Maldacena-Nunez style no-go theorem for Anti-de Sitter extrema for a range of parameters. A simple generalization incorporating 4-form flux produces axion monodromy inflation. As a relatively simple de Sitter uplift of the large-N M2-brane theory, the construction applies to de Sitter holography as well as to cosmological modeling, and introduces new connections between mathematics and the physics of string/M theory compactifications.

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  • Almost all studies of Casimir energy in Kaluza-Klein and string-theoretic contexts assume the size of extra dimensions is time-independent, primarily to identify static stable vacua.

    “Almost all of these studies assume that the size of the extra dimensions is time-independent, primarily because their objective is to identify static stable vacua.”

    From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [10]

    Sections 2 and 4 describe this paper’s use of Casimir energy to stabilize an internal volume, but they do not assess how often other Kaluza–Klein or string-theoretic studies assume time-independent extra dimensions or why they do so. Searches for static vacua and time-dependent extra dimensions found no passage addressing that broader claim. The indexed passages provide no page numbers. (LLM, conf=0.72)

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Cited by

Sorted by citations

Authors
De Luca, G. B., Silverstein, E., & Torroba, G.
Affiliations
  • Stanford University
  • Stanford University (US)
  • Bariloche Atomic Centre (AR)
ORCID
Venue
SciPost Physics
Publisher
Stichting SciPost
Published
2022-03-04
Volume
12
Issue
3
ISSN
2542-4653 (ISSN-L)
DOI
10.21468/scipostphys.12.3.083
OpenAlex
W3158607831
Cited by
39
References
4
Citations by year
2026: 8 · 2025: 5 · 2024: 9 · 2023: 13 · 2022: 3 · 2021: 1
FWCI
0.94
Type
journal article
Language
en
Open access
Licence
Locations
  • SciPost Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • BOA (University of Milano-Bicocca) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
  • Greater South Information System
Funders
  • Agencia Nacional de Promoción Científica y Tecnológica (PICT 2018-2517)
  • Comisión Nacional de Energía Atómica, Gobierno de Argentina
  • Consejo Nacional de Investigaciones Científicas y Técnicas (11220150100299)
  • National Science Foundation (PHY-1720397)
  • Simons Foundation
  • Universidad Nacional de Cuyo
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • 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
Keywords
M-theory compactification, hyperbolic manifolds, de Sitter space, cosmic acceleration, Casimir energy, Dehn filling, warped product metrics, axion monodromy inflation, de Sitter holography, M2-branes, negative curvature, tadpoles

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