The dark dimension and the Swampland

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length l∼Λ−14∼10−6m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ l\sim {\Lambda}^{-\frac{1}{4}}\sim {10}^{-6}m $$\end{document}, with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale mν∼H2Λ−112Mpl−23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m}_{\nu}\sim {\left\langle H\right\rangle}^2{\Lambda}^{-\frac{1}{12}}{M}_{\textrm{pl}}^{-\frac{2}{3}} $$\end{document}. Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev H∼Λ16Mpl13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle H\right\rangle \sim {\Lambda}^{\frac{1}{6}}{M}_{\textrm{pl}}^{\frac{1}{3}} $$\end{document}. Another prediction of the scenario is a species scale M̂∼Λ112Mpl23∼109–1010\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \hat{M}\sim {\Lambda}^{\frac{1}{12}}{M}_{\textrm{pl}}^{\frac{2}{3}}\sim {10}^9\hbox{--} {10}^{10} $$\end{document} GeV, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.