Trans-Planckian Censorship and the Swampland
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Springer
Received: January Revised: May Accepted: July Published: September
18, 31, 21, 18,
2020 2020 2020 2020
Alek Bedroya and Cumrun Vafa Jefferson Physical Laboratory, Harvard University, 17 Oxford Street, Cambridge, MA 02138, U.S.A.
E-mail: [email protected], [email protected] Abstract: In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound |V 0 | ≥ √ 2 V , which is consistent with all known cases in string theory. Like (d−1)(d−2)
the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones. Keywords: Compactification and String Models, Cosmology of Theories beyond the SM, Models of Quantum Gravity, Superstring Vacua ArXiv ePrint: 1909.11063
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)123
JHEP09(2020)123
Trans-Planckian Censorship and the Swampland
Contents 1 Introduction
1
2 The 2.1 2.2 2.3
3 3 4 4
Trans-Planckian Censorship Conjecture (TCC) Motivations for TCC Statement of TCC Immediate consequences
6 6 9 12
4 Critical points of V and quantum instabilities 4.1 Metastable dS 4.2 Unstable dS
15 15 16
5 Examples from string theory 5.1 KKLT and LVS scenarios 5.2 O(16) × O(16) Heterotic 5.3 No-go theorems in Type II theories 5.4 Energy conditions
17 17 18 19 19
6 TCC versus distance Swampland conjecture
19
7 TCC versus dS Swampland conjecture
20
8 Conclusions
21
A A strong short-field-range inequality
21
B Unstable critical points
27
C Uncertainty principle
30
1
Introduction
One of the most important challenges facing any fundamental theory of quantum gravity is how to reconcile it with the observed dark energy in our universe. The simplest possibility would be to look for a positive cosmological constant as the background describing our universe. This would necessitate that de Sitter space can exist in such a quantum theory.
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3 Consequences of TCC for scalar potentials 3.1 Long-range predictions 3.2 Generalization to multi-field models 3.3 Short-range predictions
T ≤
Mp 1 log H H
(1.1)
where H is the Hubble parameter and is related to the cosmological constant by (d−1)(d−2) 2 · H 2 = V = Λ in d spacetime dimensions. Also, for unstable critical points, we find a 1 2
See however [9] for a discussion of this. This notion is different from the similarly named phenomenon discussed in [10, 11].
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It has been difficult if not impossible to construct dS spaces (eve
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