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We examine the evolution of non-relativistic cold dark matter gravitationallycoupled to baryons with modes deep inside the Hubble radius (sub-horizonregime) using akinetic theory approach within the realm of Newtonian theory. Weobtain the general solution for the total density perturbation and we also showthat a baryon perturbation catches up with the dark matter perturbation at latetimes, which in turn makes possible the formation of bound structures. Weextend the linear perturbation analysis by considering the turn-around event,the collapse of matter, and its virialization process.

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