Constraining dark matter-baryon scattering with linear cosmology

We derive constraints on elastic scattering between baryons and dark matter using the cosmic microwave background (CMB) data from the Planck satellite and the Lyman- forest data from the Sloan Digital Sky Survey. Elastic scattering allows baryons and dark matter to exchange momentum, affecting the dynamics of linear density perturbations in the early universe. We derive constraints to scattering cross sections of the form v^n, allowing for a wide range of velocity dependencies with -42. We improve and correct previous estimates where they exist, including velocity-independent cross section as well as dark matter millicharge and electromagnetic dipole moments. Lyman- forest data dominate the constraints for n>-3, where the improvement over CMB data alone can be several orders of magnitude. Dark matter-baryon scattering cannot affect the halo mass function on mass scales M>10^12M_. Our results imply, model independently, that a baryon in the halo of a galaxy like our own Milky Way does not scatter from dark matter particles during the age of the galaxy.