The Cosmological Constant, Dark Matter and the ElectroWeak Scale meet in the Swampland

Abstract: The Swampland program, which looks for low energy theories consistent with quantum gravity, has led to the introduction of a dark dimension stemming from the cosmological constant. We show that the same argument leads to the emergence of the electroweak scale, once the dark dimension is realised in a warped background. A second warped extra dimension at the TeV scale is, therefore, postulated, where the long-standing problem of the hierarchy between the electroweak and the Planck scales can be addressed. Furthermore, standard model contributions to the cosmological constant are tamed, together with the gravitational ones. In the emergent holistic picture of gravity and gauge interactions, both Planck and the electroweak scales are emergent from a theory with two fundamental scales: $10^{-2}$ eV and $10^{10}$ GeV, which are of geometric origin and, following the Distance Conjecture, natural. Hence, a bridge is established between the two standard models of particle physics and cosmology.