  In continuation of our systematic effort to understand hadronic matter at
high density, we study dense skyrmion matter and its chiral phase structure in
an effective field theory implemented with the trace anomaly of QCD applicable
in the large $N_c$ limit. By incorporating a dilaton field $\chi$ associated
with broken conformal symmetry of QCD into the simplest form of skyrmion
Lagrangian, we simulate the effect of "sliding vacua" influenced by the
presence of matter and obtain what could correspond to the ``intrinsic
dependence" on the background of the system, i.e., matter density or
temperature, that results when a generic chiral effective field theory of
strong interactions is matched to QCD at a matching scale near the chiral scale
$\Lambda_\chi \sim 4\pi f_\pi\sim 1$ GeV. The properties of the Goldstone pions
and the dilaton scalar near the chiral phase transition are studied by looking
at the pertinent excitations of given quantum numbers on top of a skyrmion
matter and their behavior in the vicinity of the phase transition from
Goldstone mode to Wigner mode characterized by the changeover from the FCC
crystal to the half-skyrmion CC crystal. We recover from the model certain
features that are connected to Brown-Rho scaling and that suggest how to give a
precise meaning to the latter in the framework of an effective field theory
that is matched to QCD .
