Signatures of Self-Interacting Dark Matter in the Matter Power Spectrum
  and the CMB
  We consider a self-interacting dark matter model in which the massive dark
photon mediating the self-interaction decays to light dark fermions to avoid
over-closing the universe. We find that if the model is constrained to explain
the dark matter halos inferred for spiral galaxies and galaxy clusters
simultaneously, there is a strong indication that dark matter is produced
asymmetrically in the early universe. It also implies the presence of dark
radiation, late kinetic decoupling for dark matter, and a suppressed linear
power spectrum due to dark acoustic damping. The Lyman-$\alpha$ forest power
spectrum measurements put a strong upper limit on the damping scale and the
model has little room to reduce the abundances of satellite galaxies. Future
observations in the matter power spectrum and the CMB, in tandem with the
impact of self-interactions in galactic halos, makes it possible to measure the
gauge coupling and masses of the dark sector particles even when signals in
conventional dark matter searches are absent.
