Chiral phase structure at finite temperature and density in Einstein universe

The gravitational effect on the chiral phase structure at finite temperature and density is investigated in the framework of Nambu-Jona-Lasinio model in D-dimensional ultrastatic Einstein universe. In mean field approximation, the thermodynamic potential and the gap equation determining the curvature, temperature and density dependence of the chiral condensate are analytically derived. In the sense of chiral symmetry restoration and the order of the phase transition, the scalar curvature of the space-time plays similar role as the temperature.