Central density, specific energy and DM interaction rate as a function of scale factor. For the simulated DM models we show the evolution of different quantities. The central density (upper panel) and specific energy (middle panel) within a radius of r = 2.7 ckpc are shown for the DM and baryonic components. The lower panel gives the average DM interaction rate within the same radius according to Eq. (32) assuming an isotropic cross-section matched to the simulated forward dominated one with the momentum transfer cross-section (σ|_iso = 2σ_T|_iso).