  We consider the effective theory for self-interacting dark matter with
arbitrary spin and go beyond the previous discussion in the literature by
introducing a massive spin-2 particle as the mediator for the dark matter
self-scattering. We present the effective self-interactions for dark matter in
the leading order expansions with the momentum transfer and the dark matter
velocity. We compare between the Born cross section and the non-perturbative
cross section in the leading order approximation of the effective Yukawa
interaction. As a result, we find that there is a wide range of dark matter and
spin-2 particle masses for a velocity-dependent self-scattering to solve
small-scale problems at galaxies as well as satisfy the bounds from galaxy
clusters at the same time.
