We perform N-body simulations for models with a DE component. Besides of DE with constant negative state parameter w, we consider DE due to scalar fields, self-interacting through RP or SUGRA potentials. According to our post-linear analysis, at z=0, DM power spectra and halo mass functions do not depend on DE nature. This is welcome, as LCDM fits observations. Halo profiles, instead, are denser than LCDM. For example, the density at 15 kpc of a DE halo with M=10^13 exceeds LCDM by ~45%. Differences, therefore, are small but, however, DE does not ease the problem with cuspy DM profiles. We study also subhalos and find that, at $z=0$, the number of satellites coincides in all DE models. At higher z, DE models show increasing differences from LCDM and among themselves (i.e. in the mass function evolution); this is the obvious pattern to distinguish between different DE state equations.
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