  We study the pseudo phase-space density, $\rho(r)/\sigma^3(r)$, of
$\Lambda$CDM dark matter halos with and without baryons (baryons+DM, and pure
DM), by using the model introduced in Del Popolo (2009), which takes into
account the effect of dynamical friction, ordered and random angular momentum,
baryons adiabatic contraction and dark matter baryons interplay. We examine the
radial dependence of $\rho(r)/\sigma^3(r)$ over 9 orders of magnitude in radius
for structures on galactic and cluster of galaxies scales. We find that
$\rho(r)/\sigma^3(r)$ is approximately a power-law only in the range of halo
radius resolved by current simulations (down to 0.1% of the virial radius)
while it has a non-power law behavior below the quoted scale, with inner
profiles changing with mass. The non-power-law behavior is more evident for
halos constituted both of dark matter and baryons while halos constituted just
of dark matter and with angular momentum chosen to reproduce a
Navarro-Frenk-White (NFW) density profile, are characterized by an
approximately power-law behavior. The results of the present paper lead to
conclude that density profiles of the NFW type are compatible with a power-law
behavior of $\rho(r)/\sigma^3(r)$, while those flattening to the halo center,
like those found in Del Popolo (2009) or the Einasto profile, or the Burkert
profile, cannot produce radial profile of the pseudo-phase-space density that
are power-laws at all radii. The results argue against universality of the
pseudo phase-space density and as a consequence argue against universality of
density profiles constituted by dark matter and baryons as also discussed in
Del Popolo (2009).
