Abstract
There has recently been considerable interest in the question whether and under which conditions accelerated cosmological expansion can arise in the asymptotic regions of field space of a d-dimensional EFT. We conjecture that such acceleration is impossible unless there exist metastable de Sitter vacua in more than d dimensions. That is, we conjecture that ‘Asymptotic Acceleration Implies de Sitter’ (AA⇒DS). Phrased negatively, we argue that the d-dimensional ‘No Asymptotic Acceleration’ conjecture (a.k.a. the ‘strong asymptotic dS conjecture’) follows from the de Sitter conjecture in more than d dimensions. The key idea is that the relevant field-space asymptotics almost always correspond to decompactification and that the only positive energy contribution which decays sufficiently slowly in this regime is the vacuum energy of a higher-dimensional metastable vacuum. This result is in agreement with recent Swampland bounds on the potential in the asymptotics in field space from e.g. the species bound, but is significantly more constraining. We further note that for our asymptotic decompactification limits based on higher-dimensional de Sitter, the Kaluza-Klein scale always falls below the Hubble scale asymptotically. In fact, this occurs whenever \( \left|{V}^{\prime}\right|/V\le 2\sqrt{\left(d+k-2\right)/k\left(d-2\right)} \) asymptotically, with k the number of decompactifying internal directions. This is steeper than what is needed for accelerated expansion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
A. Hebecker and T. Wrase, The Asymptotic dS Swampland Conjecture — a Simplified Derivation and a Potential Loophole, Fortsch. Phys. 67 (2019) 1800097 [arXiv:1810.08182] [INSPIRE].
T.W. Grimm, C. Li and I. Valenzuela, Asymptotic Flux Compactifications and the Swampland, JHEP 06 (2020) 009 [Erratum ibid. 01 (2021) 007] [arXiv:1910.09549] [INSPIRE].
J. Calderón-Infante, I. Ruiz and I. Valenzuela, Asymptotic accelerated expansion in string theory and the Swampland, JHEP 06 (2023) 129 [arXiv:2209.11821] [INSPIRE].
D. van de Heisteeg, C. Vafa, M. Wiesner and D.H. Wu, Bounds on Field Range for Slowly Varying Positive Potentials, arXiv:2305.07701 [INSPIRE].
G. Shiu, F. Tonioni and H.V. Tran, Accelerating universe at the end of time, Phys. Rev. D 108 (2023) 063527 [arXiv:2303.03418] [INSPIRE].
G. Shiu, F. Tonioni and H.V. Tran, Late-time attractors and cosmic acceleration, Phys. Rev. D 108 (2023) 063528 [arXiv:2306.07327] [INSPIRE].
S. Cremonini et al., On asymptotic dark energy in string theory, JHEP 09 (2023) 075 [arXiv:2306.15714] [INSPIRE].
M. Cicoli, C.P. Burgess and F. Quevedo, Anisotropic Modulus Stabilisation: Strings at LHC Scales with Micron-sized Extra Dimensions, JHEP 10 (2011) 119 [arXiv:1105.2107] [INSPIRE].
M. Cicoli, F.G. Pedro and G. Tasinato, Natural Quintessence in String Theory, JCAP 07 (2012) 044 [arXiv:1203.6655] [INSPIRE].
M. Cicoli et al., De Sitter vs Quintessence in String Theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
Y. Olguin-Trejo, S.L. Parameswaran, G. Tasinato and I. Zavala, Runaway Quintessence, Out of the Swampland, JCAP 01 (2019) 031 [arXiv:1810.08634] [INSPIRE].
A. Hebecker, T. Skrzypek and M. Wittner, The F -term Problem and other Challenges of Stringy Quintessence, JHEP 11 (2019) 134 [arXiv:1909.08625] [INSPIRE].
W. Fischler, A. Kashani-Poor, R. McNees and S. Paban, The Acceleration of the universe, a challenge for string theory, JHEP 07 (2001) 003 [hep-th/0104181] [INSPIRE].
S. Hellerman, N. Kaloper and L. Susskind, String theory and quintessence, JHEP 06 (2001) 003 [hep-th/0104180] [INSPIRE].
D. Andriot, D. Tsimpis and T. Wrase, Accelerated expansion of an open universe, and string theory realizations, arXiv:2309.03938 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
F. Denef, A. Hebecker and T. Wrase, de Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].
D. Andriot and C. Roupec, Further refining the de Sitter swampland conjecture, Fortsch. Phys. 67 (2019) 1800105 [arXiv:1811.08889] [INSPIRE].
D. Junghans, Weakly Coupled de Sitter Vacua with Fluxes and the Swampland, JHEP 03 (2019) 150 [arXiv:1811.06990] [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09 (2020) 123 [arXiv:1909.11063] [INSPIRE].
T. Rudelius, Dimensional reduction and (Anti) de Sitter bounds, JHEP 08 (2021) 041 [arXiv:2101.11617] [INSPIRE].
T. Rudelius, Asymptotic observables and the swampland, Phys. Rev. D 104 (2021) 126023 [arXiv:2106.09026] [INSPIRE].
D. Andriot, N. Cribiori and D. Erkinger, The web of swampland conjectures and the TCC bound, JHEP 07 (2020) 162 [arXiv:2004.00030] [INSPIRE].
M. Cicoli, F. Cunillera, A. Padilla and F.G. Pedro, Quintessence and the Swampland: The Numerically Controlled Regime of Moduli Space, Fortsch. Phys. 70 (2022) 2200008 [arXiv:2112.10783] [INSPIRE].
M. Cicoli, F. Cunillera, A. Padilla and F.G. Pedro, Quintessence and the Swampland: The Parametrically Controlled Regime of Moduli Space, Fortsch. Phys. 70 (2022) 2200009 [arXiv:2112.10779] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless Strings and the Weak Gravity Conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings from infinite distance limits, JHEP 02 (2022) 190 [arXiv:1910.01135] [INSPIRE].
C.F. Cota, A. Mininno, T. Weigand and M. Wiesner, The asymptotic Weak Gravity Conjecture for open strings, JHEP 11 (2022) 058 [arXiv:2208.00009] [INSPIRE].
M. Wiesner, Light strings and strong coupling in F-theory, JHEP 04 (2023) 088 [arXiv:2210.14238] [INSPIRE].
M. Cicoli, G. Dibitetto and F.G. Pedro, New accelerating solutions in late-time cosmology, Phys. Rev. D 101 (2020) 103524 [arXiv:2002.02695] [INSPIRE].
M. Cicoli, G. Dibitetto and F.G. Pedro, Out of the Swampland with Multifield Quintessence?, JHEP 10 (2020) 035 [arXiv:2007.11011] [INSPIRE].
M. Brinkmann, M. Cicoli, G. Dibitetto and F.G. Pedro, Stringy multifield quintessence and the Swampland, JHEP 11 (2022) 044 [arXiv:2206.10649] [INSPIRE].
M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].
M. Etheredge et al., Sharpening the Distance Conjecture in diverse dimensions, JHEP 12 (2022) 114 [arXiv:2206.04063] [INSPIRE].
T. Rudelius, Asymptotic scalar field cosmology in string theory, JHEP 10 (2022) 018 [arXiv:2208.08989] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
L. Alvarez-Gaume, P.H. Ginsparg, G.W. Moore and C. Vafa, An O(16) × O(16) Heterotic String, Phys. Lett. B 171 (1986) 155 [INSPIRE].
S. Hellerman and I. Swanson, Cosmological solutions of supercritical string theory, Phys. Rev. D 77 (2008) 126011 [hep-th/0611317] [INSPIRE].
M.N.R. Wohlfarth, Inflationary cosmologies from compactification?, Phys. Rev. D 69 (2004) 066002 [hep-th/0307179] [INSPIRE].
J.G. Russo and P.K. Townsend, Late-time Cosmic Acceleration from Compactification, Class. Quant. Grav. 36 (2019) 095008 [arXiv:1811.03660] [INSPIRE].
P. Marconnet and D. Tsimpis, Universal accelerating cosmologies from 10d supergravity, JHEP 01 (2023) 033 [arXiv:2210.10813] [INSPIRE].
F. Apers, J.P. Conlon, M. Mosny and F. Revello, Kination, meet Kasner: on the asymptotic cosmology of string compactifications, JHEP 08 (2023) 156 [arXiv:2212.10293] [INSPIRE].
T. Van Riet, On classical de Sitter solutions in higher dimensions, Class. Quant. Grav. 29 (2012) 055001 [arXiv:1111.3154] [INSPIRE].
D. Andriot and L. Horer, (Quasi-) de Sitter solutions across dimensions and the TCC bound, JHEP 01 (2023) 020 [arXiv:2208.14462] [INSPIRE].
N. Cribiori and C. Montella, Quantum gravity constraints on scale separation and de Sitter in five dimensions, JHEP 05 (2023) 178 [arXiv:2303.04162] [INSPIRE].
M. Montero, T. Van Riet and G. Venken, A dS obstruction and its phenomenological consequences, JHEP 05 (2020) 114 [arXiv:2001.11023] [INSPIRE].
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, Trans-Planckian Censorship and Inflationary Cosmology, Phys. Rev. D 101 (2020) 103502 [arXiv:1909.11106] [INSPIRE].
A.R. Liddle, A. Mazumdar and F.E. Schunck, Assisted inflation, Phys. Rev. D 58 (1998) 061301 [astro-ph/9804177] [INSPIRE].
M. Cicoli, S. de Alwis and A. Westphal, Heterotic Moduli Stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].
Acknowledgments
We thank Timo Weigand, Michele Cicoli, Filippo Revello, Gary Shiu, Flavio Tonioni, and Irene Valenzuela for valuable discussion. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 — 390900948 (the Heidelberg STRUCTURES Excellence Cluster).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2306.17213
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hebecker, A., Schreyer, S. & Venken, G. No asymptotic acceleration without higher-dimensional de Sitter vacua. J. High Energ. Phys. 2023, 173 (2023). https://doi.org/10.1007/JHEP11(2023)173
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2023)173