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 ρswamp ∼ mKK4 between the vacuum energy ρswamp and the size of the extra dimension mKK-1 (mKK is the mass scale of a Kaluza-Klein tower), and on the corresponding result ρEFT from the effective field theory (EFT) limit. We show that ρEFT 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 ρEFT ∼ mKK4 (with no need for fine-tuning). This renders the matching between ρswamp and ρEFT a nontrivial 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.