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\sim {\Lambda}^{-\frac{1}{4}}\sim {10}^{-6}m $, 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 $ {m}_{\nu}\sim {\left\langle H\right\rangle}^2{\Lambda}^{-\frac{1}{12}}{M}_{\textrm{pl}}^{-\frac{2}{3}} $. 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 $ \left\langle H\right\rangle \sim {\Lambda}^{\frac{1}{6}}{M}_{\textrm{pl}}^{\frac{1}{3}} $. Another prediction of the scenario is a species scale $ \hat{M}\sim {\Lambda}^{\frac{1}{12}}{M}_{\textrm{pl}}^{\frac{2}{3}}\sim {10}^9\hbox{--} {10}^{10} $ 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 ~10$^{11}$ GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.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 $l\sim \Lambda^{-\frac{1}{4}}\sim 10^{-6}\, m$, 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 $m_{\nu}\sim \langle H\rangle^2\, \Lambda^{-\frac{1}{12}}M_{pl}^{-\frac{2}{3}}$. 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 $\langle H\rangle \sim \Lambda^{\frac{1}{6}}M_{pl}^{\frac{1}{3}}$. Another prediction of the scenario is a species scale ${\hat M} \sim \Lambda^ {\frac{1}{12}}M_{pl}^{\frac{2}{3}}\sim 10^{9}-10^{10} GeV$, 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 $\sim 10^{11}\, GeV$. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays