Finite-Size Dark Matter and its Effect on Small-Scale Structure

If dark matter has a finite size that is larger than its Compton wavelength, the corresponding self-interaction cross section decreases with the velocity. We investigate the implications of this puffy dark matter for addressing the small-scale problems of the Λ cold dark matter model and show that the way the nonrelativistic cross section varies with the velocity is largely independent of the dark matter internal structure. Even in the presence of a light particle mediating self-interactions, we find that the finite-size effect may dominate the velocity dependence. We present an explicit example in the context of a QCD-like theory and discuss possible ways to differentiate puffy dark matter from the usual light-mediator scenarios. Particularly relevant for this are low-threshold direct-detection experiments and indirect signatures associated with the internal structure of dark matter.