  It has recently been suggested that in a brane world scenario with large
extra dimensions, short distance gravitational interactions can enhance the
dark matter scattering cross-section in a velocity dependent way. Such a
modification may then help to address possible problems with non-interacting
cold dark matter on galactic and sub-galactic scales. We argue that,
considering the singular character of the higher dimensional Newtonian
potential, the scattering cross-section is UV-dependent, depending ultimately
on the underlying quantum gravity theory considered. We demonstrate that for a
wide class of unitary short distance regularizations, the actual cross-section
is velocity-independent and does not significantly affect dark matter
substructure. We comment on the problem of thermalization of ultra-light cold
dark matter by gravitational interactions in the early universe.
