Upper panel: testing the redshift evolution of the self-similar scaling of the dark matter density distribution with the variable overdensity scaling model. The density profiles are given for redshifts of z = 0 (heavy line) and z = 0.2521, 0.5073, 0.7695, 1.0013. Dashed lines show the unscaled and solid lines the scaled profiles. Lower panel: redshift evolution of the self-similar scaling of the dark matter density distribution with the fixed overdensity scaling model. This model clearly is better than the model shown above. We also show, displaced by a factor of 0.1, the density profiles after applying the full scaling corrections described in Sect. 5. Apart from some numerical fluctuations we observe a perfect fit of the scaling corrections.