  Given a closed smooth manifold M which carries a positive scalar curvature
metric, one can associate an abelian group P(M) to the space of positive scalar
curvature metrics on this manifold. The group of all diffeomorphisms of the
manifold naturally acts on P(M). The moduli group of positive scalar curvature
metrics is defined to be the quotient abelian group of this action, i.e. the
coinvariant of the action. The moduli group measures the size of the moduli
space of positive scalar curvature metrics on M. In this paper, we use the
higher rho invariant and the finite part of the K-theory of the group
C*-algebra of the fundamental group of M to give a lower bound of the rank of
the moduli group.
