  We explore the cosmology of the Dark Dimension scenario taking into account
perturbations in the linear regime. In the context of the Dark Dimension
scenario, a natural candidate for dark matter in our universe is the
excitations of a tower of massive spin-2 KK gravitons. These dark gravitons are
produced in the early universe and decay to lighter KK gravitons during the
course of cosmological evolution. The decay causes the average dark matter mass
to decrease as the universe evolves. In addition, the kinetic energy liberated
in each decay leads to a kick velocity for the dark matter particles leading to
a suppression of structure formation. Using current CMB (Planck), BAO and
cosmic shear (KiDS-1000) data, we put a bound on the dark matter kick velocity
today $v_\mathrm{today} \leq 2.2 \times 10^{-4} c$ at 95\% CL. This leads to
rather specific regions of parameter space for the dark dimension scenario. The
combination of the experimental bounds from cosmology, astrophysics and
table-top experiments lead to the range $l_5\sim 1- 10 \, \mu m$ for the size
of the Dark Dimension. The Dark Dimension scenario is found to be remarkably
consistent with current observations and provides signatures that are within
reach of near-future experiments.
