Dynamics of Dark Matter in Baryon-Radiation Plasma: Perspectives using Meschersky equation

Abstract: With an aim to argue for the truly collisionless nature of cold dark matter between epochs of equality and recombination, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Meschersky equation to describe the dynamics of cold dark matter in the presence of varying mass of strongly coupled baryon-radiation plasma. Based on this model, we discuss the growth of perturbations in cold dark matter both in the Jeans theory and in the expanding universe using Newton's theory. We see the effect of the perturbations in the cold dark matter potential on the cosmic microwave background anisotropy that originated at redshifts between equality and recombination i.e. $1100 < z < z_{eq}$. Also we obtain an expression for the Sachs-Wolfe effect, i.e. the CMB temperature anisotropy at decoupling in terms of the perturbations in cold dark matter potential. We obtain similar solutions both in the static and in the expanding universe, for epochs of recombination. From this, we infer about the time scale when the dark energy starts to dominate.