Self-Interacting Cold Dark Matter: A New Jeans Theory Based Model

We explore the low-energy cosmological dynamics of self-interacting cold dark matter (CDM). We argue in favor of the truly collisionless nature of CDM, which is self-interacting at small scales between epochs of equality and recombination. For this, we assume a model wherein a strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Merscerskii equation i.e., the variable mass formalism of classical dynamics. We obtain new results relating the oscillations in the CMB anisotropy to the ejection velocity of the baryon-radiation plasma, which can be a useful tool for numerical work for exploring the second peak of the CMB. Based on this model, we discuss the growth of perturbations in such a self-interacting CDM both in the Jeans theory and in the expanding universe using Newton's theory. We obtain an expression for the growth of fractional perturbations in CDM, which reduce to the standard result of perturbation theory for late recombination epochs. We see the effect of the average of the perturbations in the CDM potential on the cosmic microwave background temperature anisotropy that originated at redshifts between equality and recombination i.e., 1100 < z < z(eq). We also we obtain an expression for the Sachs-Wolfe effect, i.e., the CMB temperature anisotropy at decoupling in terms of the average of the perturbations in the CDM potential.