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We explore the low energy cosmological dynamics of feebly self-interactingcold dark matter and propose a new simple explanation for the rotation curvesof the core-halo model in massive LSB (Low Surface brightness)galaxies. Weargue in favor of the truly collisionless nature of cold dark matter,which isfeebly,self-interacting at small scales between epochs of equality andrecombination.For this, we assume a model, wherein strongly coupledbaryon-radiation plasma ejects out of small regions of concentrated cold darkmatter without losing its equilibrium. We use the Merscerskii equation i.e. thevariable mass formalism of classical dynamics.We obtain new results relatingthe oscillations in the CMB anisotropy to the ejection velocity of thebaryon-radiation plasma,which can be useful tool for numerical work forexploring the second peak of CMB. Based on this model, we discuss the growth ofperturbations in such a feebly self-interacting,cold dark matter both in theJeans theory and in the expanding universe using Newton's theory.We obtain anexpression for the growth of fractional perturbations in cold dark matter,whichreduce to the standard result of perturbation theory for late recombinationepochs. We see the effect of the average of the perturbations in the cold darkmatter potential on the cosmic microwave background temperature anisotropy thatoriginated 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 CMBtemperature anisotropy at decoupling in terms of the average of theperturbations in cold dark matter potential.

Feebly Self-Interacting Cold Dark Matter: New theory for the Core-Halo structure in GLSB Galaxies