Using kinetic theory to examine a self-gravitating system composed of baryons and cold dark matter

We examine the evolution of non-relativistic cold dark matter gravitationally coupled to baryons with modes deep inside the Hubble radius (sub-horizon regime) using a kinetic theory approach within the realm of Newtonian theory. We obtain the general solution for the total density perturbation and we also show that a baryon perturbation catches up with the dark matter perturbation at late times, which in turn makes possible the formation of bound structures. We extend the linear perturbation analysis by considering the turn-around event, collapse of matter, and its virialization process.