  We consider cosmological aspects of the Dark Dimension (a mesoscopic
dimension of micron scale), which has recently been proposed as the unique
corner of the quantum gravity landscape consistent with both the Swampland
criteria and observations. In particular we show how this leads, by the
universal coupling of the Standard Model sector to bulk gravitons, to massive
spin 2 KK excitations of the graviton in the dark dimension (the "dark
gravitons") as an unavoidable dark matter candidate. Assuming a lifetime for
the current de Sitter phase of our universe of order Hubble, which follows from
both the dS Swampland Conjecture and TCC, we show that generic features of the
dark dimenson cosmology can naturally lead to the correct dark matter density
and a resolution of the cosmological coincidence problem, where the
matter/radiation equality temperature ($T\sim$ 1 eV) coincides with the
temperature where the dark energy begins to dominate. Thus one does not need to
appeal to Weinberg's anthropic argument to explain this coincidence. The dark
gravitons are produced at $T\sim$ 4 GeV, and their composition changes as they
mainly decay to lighter gravitons, without losing much total mass density. The
mass of dark gravitons is $m_{\text{DM}}\sim 1-100$ keV today.
