  The mean-field level calculation shows that the QCD matter can have multiple
critical points incorporating the color superconductivity under charge
neutrality constraint due to the repulsive vector interaction; this actually
implies that the QCD matter is very soft for a simultaneous formation of
diquark and chiral condensates coupled with the baryonic density. Dynamical
density fluctuations are analyzed as possible soft modes around the QCD
critical point using dissipative relativistic fluid dynamics. It is found that
the entropy fluctuation solely gets enhanced while the sound modes due to
mechanical density fluctuations are strongly attenuated around the QCD CP,
which may suggest a suppression or even total disappearance of Mach cone at the
CP.
