
As the first in a series of systematic work on dense hadronic matter, we study the properties of the pion in dense medium using Skyrme's effective Lagrangian as a unified theory of the hadronic interactions applicable in the large Nc limit. Dense baryonic matter is described as the ground state of a skyrmion matter which appears in two differentiated phases as a function of matter density: (i) at high densities as a stable cubiccentered (CC) halfskyrmion crystal; (ii) at low densities as an unstable facecentered cubic (FCC) skyrmion crystal. We substitute the latter by a stable inhomogeneous phase of lumps of dense matter, which represents a naive Maxwell construction of the phase transition. This baryonic dense medium serves as a background for the pions whose effective inmedium Lagrangian we construct by allowing timedependent quantum fluctuations on the classical dense matter field. We find that the same parameter which describes the phase transition for baryonic matter, the expectation value of the σ field, also describes the phase transition for the dynamics of the inmedium pion. Thus, the structure of the baryonic ground state crucially determines the behavior of the pion in the medium. As matter density increases, 〈σ〉 decreases, a phenomenon which we interpret to signal, in terms of the parameters of the effective pion Lagrangian and , the restoration of chiral symmetry at high density. Our calculation shows also the important role played by the higher powers in the density as it increases and chiral symmetry is being restored. This feature is likely to be generic at high density although our ground state may not be the true ground state.
