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

TL;DR

This paper critically examines the 'dark dimension' scenario linked to the cosmological constant, revealing UV-sensitive terms in effective field theory calculations that challenge previous assumptions and highlight the need for mechanisms to suppress these terms.

Contribution

It identifies previously overlooked UV-sensitive contributions in EFT calculations of vacuum energy, questioning the validity of the dark dimension hypothesis based on existing literature.

Findings

UV-sensitive terms invalidate the simple $ ho_{EFT} o m_{KK}^4$ relation

Matching $ ho_{swamp}$ and $ ho_{EFT}$ is more complex than previously thought

A mechanism is needed to suppress UV-sensitive contributions for consistency

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 $\rho_{\rm swamp}\sim m_{_{\rm KK}}^4$ between the vacuum energy $\rho_{\rm swamp}$ and the size of the extra dimension $m_{_{\rm KK}}^{-1}$ ($m_{_{\rm KK}}$ is the mass scale of a Kaluza-Klein tower), and on the corresponding result $\rho_{_{\rm EFT}}$ from the EFT limit. We show that $\rho_{_{\rm EFT}}$ 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 $\rho_{_{\rm EFT}}\sim m_{_{\rm KK}}^4$ (with no need for fine-tuning). This renders the matching between $\rho_{\rm swamp}$ and $\rho_{_{\rm EFT}}$ 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.