Abstract
We study whether the universal runaway behaviour of stringy scalar potentials towards infinite field distance limits can produce an accelerated expanding cosmology à la quintessence. We identify a loophole to some proposed bounds that forbid such asymptotic (at parametric control) accelerated expansion in 4d \( \mathcal{N} \) = 1 supergravities, by considering several terms of the potential competing asymptotically. We then analyse concrete string theory examples coming from F-theory flux compactifications on Calabi-Yau fourfolds, extending previous results by going beyond weak string coupling to different infinite distance limits in the complex structure moduli space. We find some potential candidates to yield asymptotic accelerated expansion with a flux potential satisfying \( \gamma =\frac{\left\Vert \nabla V\right\Vert }{V}<\sqrt{2} \) along its gradient flow. However, whether this truly describes an accelerated expanding cosmology remains as an open question until full moduli stabilization including the Kahler moduli is studied. Finally, we also reformulate the condition for forbidding asymptotic accelerated expansion as a convex hull de Sitter conjecture which resembles a convex hull scalar WGC for the membranes generating the flux potential. This provides a pictorial way to quickly determine the asymptotic gradient flow trajectory in multi-moduli setups and the value of γ along it.
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Acknowledgments
We would like to thank Thomas Grimm, Damian van de Heisteeg, Luis Ibáñez, Fernando Marchesano, Miguel Montero, David Prieto, Tom Rudelius and Ángel Uranga for useful discussions. The authors acknowledge the support of the Spanish Agencia Estatal de Investigacion through the grant IFT Centro de Excelencia Severo Ochoa CEX2020-001007-S and the grants PGC2018-095976-B-C21 and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/ 501100011033 and by ERDF A way of making Europe. The work of I.V. is partly supported by the grant RYC2019-028512-I from the MCI (Spain). The work of I.R. is supported by the Spanish FPI grant No. PRE2020-094163. The work by J.C. is supported by the FPU grant no. FPU17/04181 from the Spanish Ministry of Education.
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Calderón-Infante, J., Ruiz, I. & Valenzuela, I. Asymptotic accelerated expansion in string theory and the Swampland. J. High Energ. Phys. 2023, 129 (2023). https://doi.org/10.1007/JHEP06(2023)129
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DOI: https://doi.org/10.1007/JHEP06(2023)129