  We apply the strategy to study of diffeomorphisms via block diffeomorphisms
to the world of positive scalar curvature (psc) metrics. For each closed psc
manifold $M$, we construct the cubical set
$\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$ of all psc block metrics, which only
encodes concordance information of psc metrics within its homotopy type. We
show that $\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$ is a cubical Kan set, give
a geometric description for the group structure of the combinatorial homotopy
groups, and construct a comparison map from the cubical model
$\mathcal{R}^+_{\bullet}(M)$ of the space of psc metrics on $M$ to
$\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$. Next, we build a concordance-themed
model for real $K$-theory based on the notion of invertible block Dirac
operators and use it to factor the index difference through
$\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$. In the final part of this thesis,
we construct the psc Hatcher spectral sequence, which is a non-index-theoretic
tool to get information about the difference of $\mathcal{R}^+_{\bullet}(M)$
and $\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$.
