  The extended Linear Sigma Model (eLSM) is an effective model of QCD which
includes in the mesonic sector (pseudo)scalar and (axial-)vector quarkonia
mesons as well as one dilaton/glueball field and in the baryonic sector the
nucleon doublet and its chiral partner in the mirror assignment. The chiral
partner of the pion turns out to be the resonance $f_{0}(1370),$ which is then
predominantly a quarkonium state. As a consequence, $f_{0}(500)$ is
predominately not a quarkonium state but a four-quark object and is at first
not part of the model. Yet, $f_{0}(500)$ is important in the baryonic sector
and affects nuclear matter saturation, the high-density behavior, and
nucleon-nucleon scattering. In these proceedings, we show how to enlarge the
two-flavour version of the eLSM in order to include the four-quark field
$f_{0}(500)$ in a chiral invariant manner. We then discuss homogeneous and
inhomogeneous chiral restoration in a dense medium.
