Constraining strong baryon–dark-matter interactions with primordial nucleosynthesis and cosmic rays

Self-interacting dark matter (SIDM) was introduced by Spergel and Steinhardt to address possible discrepancies between collisionless dark matter simulations and observations on scales of less than 1 Mpc. We examine the case in which dark matter particles not only have strong self-interactions but also have strong interactions with baryons. The presence of such interactions will have direct implications for nuclear and particle astrophysics. Among these are a change in the predicted abundances from big bang nucleosynthesis (BBN) and the flux of $\gamma$ rays produced by the decay of neutral pions which originate in collisions between dark matter and galactic cosmic rays (CR). From these effects we constrain the strength of the baryon–dark-matter interactions through the ratio of baryon–dark-matter interaction cross section to dark matter mass, s. We find that BBN places a weak upper limit on this ratio $\lesssim {10}^8\hspace{0.5em}{\mathrm{cm}}^2{\mathrm{g}}^{-1}.$ CR-SIDM interactions, however, limit the possible DM-baryon cross section to $\lesssim 5\times {10}^{-3}\hspace{0.5em}{\mathrm{cm}}^2{\mathrm{g}}^{-1};$ this rules out an energy-independent interaction, but not one which falls with center-of-mass velocity $s\propto 1/v$ or steeper.