  We study the cosmological predictions of the dark D-brane model, in which
dark matter resides on a D-brane moving in a higher-dimensional space. By
construction, dark matter interacts only gravitationally with the standard
model sector in this framework. The dark energy scalar field is associated with
the position of the D-brane, and its dynamics is encoded in a Dirac-Born-Infeld
action. On the other hand, dark matter is identified with matter on the
D-brane, that naturally couples to dark energy \textit{via} a disformal
coupling. We analyse the numerical evolution of the cosmological background,
highlighting the fact that there are two regimes of interest: one, in which the
coupling is positive throughout; and another, in which the coupling is negative
at the present. In the latter, there is the enticing possibility of having
scenarios in which the coupling is positive for a significant part of the
evolution, before decreasing towards negative values. In both cases, the
coupling is very small at early times, and only starts to grow during the late
matter dominated era. We also derive the equations for the linear cosmological
perturbations, an expression for the effective time-dependent gravitational
coupling between dark matter particles and present the numerical results for
the CMB anisotropy and matter power spectra. This allows for a direct
comparison of the predictions for the growth of large scale structure with
other disformal quintessence models.
