Does the cosmological constant really indicate the existence of a dark dimension?
Carlo Branchina, Vincenzo Branchina, Filippo Contino, Arcangelo Pernace
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 [Formula: see text] between the vacuum energy [Formula: see text] and the size of the extra dimension [Formula: see text] ([Formula: see text] is the mass scale of a Kaluza–Klein tower), and on the corresponding result [Formula: see text] from the effective field theory (EFT) limit. We show that [Formula: see text] 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 [Formula: see text] (with no need for fine-tuning). This renders the matching between [Formula: see text] and [Formula: see text] 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.