Does the Cosmological Constant really indicate the existence of a Dark Dimension?

Abstract

According to the "dark dimension" (DD) scenario, we might live in a universe with a single compact extra dimension, whose mesoscopic size is dictated by the measured value of the cosmological constant. This scenario is based on swampland conjectures, that lead to the relation ${\rho }_{\mathrm{swamp}}\sim m_{{}_{\mathrm{KK}}}^4$ between the vacuum energy ${\rho }_{\mathrm{swamp}}$ and the size of the extra dimension $m_{{}_{\mathrm{KK}}}^{-1}$ ($m_{{}_{\mathrm{KK}}}$ is the mass scale of a Kaluza-Klein tower), and on the corresponding result ${\rho }_{{}_{\mathrm{EFT}}}$ from the EFT limit. We show that ${\rho }_{{}_{\mathrm{EFT}}}$ contains previously missed UV-sensitive terms, whose presence invalidates the widely spread belief (based on existing literature) that the calculation gives automatically the finite result ${\rho }_{{}_{\mathrm{EFT}}}\sim m_{{}_{\mathrm{KK}}}^4$ (with no need for fine-tuning). This renders the matching between ${\rho }_{\mathrm{swamp}}$ and ${\rho }_{{}_{\mathrm{EFT}}}$ a non-trivial issue. We then comment on the necessity to find a mechanism that implements the suppression of the aforementioned UV-sensitive terms. This should finally allow to frame the DD scenario in a self-consistent framework, also in view of its several phenomenological applications based on EFT calculations.

arXiv comment18 pages; 1 Appendix. Accepted for publication in International Journal of Geometric Methods in Modern Physics (DOI:10.1142/S0219887824503055)

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• Dark Dimension and the Effective Field Theory limit
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