  The fundamental properties of dense nuclear matter, as it exists in the core
of massive stellar objects, are still largely unknown. The investigation of the
high-density equation of state (EOS), which determines mass and radii of
neutron stars and the dynamics of neutron star mergers, is in the focus of
astronomical observations and of laboratory experiments with heavy-ion
collisions. Moreover, the microscopic degrees-of-freedom of strongly
interacting matter at high baryon densities are also unknown. While
Quantum-Chromo-Dynamics (QCD) calculations on the lattice find a smooth chiral
crossover between hadronic matter and the quark-gluon plasma for high
temperatures at zero baryon chemical potential, effective models predict a 1st
order chiral transition with a critical endpoint for matter at large baryon
chemical potentials. Up to date, experimental data both on the high-density EOS
and on a possible phase transition in dense baryonic matter are very scarce. In
order to explore this terra incognita, dedicated experimental programs are
planned at future heavy-ion research centres: the CBM experiment at FAIR, and
the MPD and BM@N experiments at NICA. The research programs and the layout of
these experiments will be presented. The future results of these laboratory
experiments will complement astronomical observations concerning the EOS, and,
in addition, will shed light on the microscopic degrees of freedom of QCD
matter at neutron star core densities.
