  Let $M$ be a simply connected spin manifold of dimension at least six which
admits a metric of positive scalar curvature. We show that the observer moduli
space of positive scalar curvature metrics on $M$ has non-trivial higher
homotopy groups.
  Moreover, denote by $\mathcal{M}_0^+(M)$ the moduli space of positive scalar
cuvature metrics on $M$ associated to the group of orientation-preserving
diffeomorphisms of $M$. We show that if $M$ belongs to a certain class of
manifolds which includes $(2n-2)$-connected $(4n-2)$-dimensional manifolds,
then the fundamental group of $\mathcal{M}_0^+(M)$ is non-trivial.
