Abstract
One of the unique features of quantum gravity is the lack of local observables and the completeness of boundary observables. We show that the existence of boundary observables for particles with masses \( \underset{t-\infty }{\lim}\frac{m}{H}=\infty \) in scalar fieldcosmologies where a(t) ∼ tp is equivalent to TCC, which implies p ≤ 1. Moreover, the mass of weakly-coupled particles must decay like m ≲ t1 − 2p to ensure that they yield non-trivial boundary observables. This condition can be expressed in terms of the scalar field that drives the cosmology as m ≲ exp(−cϕ) where c depends on the scalar potential. The strongest bound we find is achieved for \( V\sim \exp \left(-2\phi /\sqrt{d-2}\right) \) where \( c=1/\sqrt{d-2} \). These results connect some of the most phenomenologically interesting Swampland conjectures to the most basic version of holography.
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Acknowledgments
We are grateful for countless productive discussions with Georges Obied that were essential to sharpening the core idea of this work. We thank Rashmish Mishra, Miguel Montero, John Stout, and Cumrun Vafa for helpful discussions. We thank Austin Joyce, Hayden Lee, Georges Obied, and Cumrun Vafa for valuable comments on the earlier versions of this article. The work of AB is supported by a grant from the Simons Foundation (602883, CV) and by the NSF grant PHY-2013858.
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Bedroya, A. Holographic origin of TCC and the distance conjecture. J. High Energ. Phys. 2024, 16 (2024). https://doi.org/10.1007/JHEP06(2024)016
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DOI: https://doi.org/10.1007/JHEP06(2024)016