The dark dimension and the Swampland

Abstract

Abstract 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 $$ l\sim {\Lambda}^{-\frac{1}{4}}\sim {10}^{-6}m $$ l ∼ Λ − 1 4 ∼ 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 $$ {m}_{\nu}\sim {\left\langle H\right\rangle}^2{\Lambda}^{-\frac{1}{12}}{M}_{\textrm{pl}}^{-\frac{2}{3}} $$ m ν ∼ H 2 Λ − 1 12 M pl − 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 $$ \left\langle H\right\rangle \sim {\Lambda}^{\frac{1}{6}}{M}_{\textrm{pl}}^{\frac{1}{3}} $$ H ∼ Λ 1 6 M pl 1 3 . Another prediction of the scenario is a species scale $$ \hat{M}\sim {\Lambda}^{\frac{1}{12}}{M}_{\textrm{pl}}^{\frac{2}{3}}\sim {10}^9\hbox{--} {10}^{10} $$ M ̂ ∼ Λ 1 12 M pl 2 3 ∼ 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 ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.