  In this paper, we study how the presence of bulge formation in galaxies
influence their inner density profile, by means of an extended version of the
Del Popolo (2009) semi-analytical model. As in Del Popolo (2009), the model
takes into account the effect of baryons adiabatic contraction, ordered and
random angular momentum, dynamical friction, and adds to the previous the
effect of gas cooling, star formation, supernova feedback, and reionization.
Our model shows that dwarf galaxies are bulgeless, in agreement with
observations showing that the large majority of them has no stellar bulges, and
are characterized by a flat profile well described by a Burkert profile. {We
then studied the effect of a bulge, added to the {cored} DM halo, on the
density profile}. In the case of a galaxy having a mass $10^{11} M_{\odot}$ the
inner density profile has a slope $\alpha \simeq 0.65$, for a bulge of $4.5
\times 10^{9} M_{\odot}$, while if bulge formation is not considered, the slope
would be $\alpha \simeq 0.55$. If the bulge is larger, $6.5 \times 10^{9}
M_{\odot}$ the slope is $\alpha \simeq 0.7$. In the case of a larger galaxy
with $10^{12} M_{\odot}$ the slope is $\alpha \simeq 0.85$, while in absence of
bulge it is $\alpha \simeq 0.75$. We finally study how the inner slope $\alpha$
changes with the bulge mass, and we find a correlation among the two
quantities. The result shows that bulge formation has an important role in
shaping the inner DM density profile in agreement with Inoue & Saitoh (2011)
result. The result implies that going from Sc to SO Hubble type the slope is
slightly steepening due to the bulge formation, and due to the fact that early
type galaxies have larger bulges.
