Dark dimension and the standard model landscape

We study the landscape of lower -dimensional vacua of the standard model (SM) coupled to gravity in the presence of the so-called "dark dimension" of size RI in the micron range, focusing on the validity of the swampland conjecture forbidding the presence of nonsupersymmetric anti-de Sitter (AdS) vacua in a consistent quantum gravity theory. We first adopt the working assumption that right-handed neutrinos propagate in the bulk, so that neutrino Yukawa couplings become tiny due to a volume suppression, leading to naturally light Dirac neutrinos. We show that the neutrino Kaluza-Klein (KK) towers compensate for the graviton tower to maintain stable de Sitter (dS) vacua found in the past, but neutrino oscillation data set restrictive bounds on R-perpendicular to and therefore the first KK neutrino mode is too heavy to alter the shape of the radion potential or the required maximum mass for the lightest neutrino to carry dS rather than AdS vacua found in the absence of the dark dimension, m(1;max) < 7.63 meV. We also show that a very light gravitino (with mass in the meV range) could help relax the neutrino mass constraint m(1;max) < 50 meV. The differences for the predicted total neutrino mass Sigma m(nu )among these two scenarios are within reach of nextgeneration cosmological probes that may measure the total neutrino mass with an uncertainty sigma(Sigma m(nu)) = 0.014 eV. We also demonstrate that the KK tower of a very light gravitino can compensate for the graviton tower to sustain stable dS vacua and thus right-handed neutrinos can (in principle) be locked on the brane. For this scenario, Majorana neutrinos could develop dS vacua, which is not possible in the SM coupled to gravity. Finally, we investigate the effects of bulk neutrino masses in suppressing oscillations of the zero modes into the first KK modes to relax the oscillation bound on R-perpendicular to.