  A fluid of Skyrmions coupled to the dilaton field and the $\o$ meson field is
considered. A mean field theory is developed in which the dilaton and the $\o$
field acquire a mean value determined by the Skyrmions. The influence of the
background fields on the Skyrmion profile is determined and consequently the
scaling properties of the Skyrmion follow. The model obeys chiral invariance
and scale invariance broken only by the dilaton trace anomaly potential. The
dilaton plays the role of the scalar field as in the $\s + \o$ model. The
dilaton potential is augmented by terms that do not spoil the trace anomaly
while allowing a fit to nuclear matter properties. The phase diagram of the
model shows unique features, like a lack of solutions for certain densities and
temperatures, signalling the appearance of a new phase that can not be
described in terms of Skyrme baryons.
