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 $\Lambda$CDM model. In particular, we show that the way the non-relativistic cross section varies with the velocity is largely independent of the dark matter internal structure when the range of the mediating force is very short. We present an explicit example in the context of a QCD-like theory of dark matter and show that low-threshold direct detection experiments have the potential to probe Puffy Dark Matter.