On the topology of the moduli space of positive scalar curvature concordances

Let M be a manifold which admits a metric with positive scalar curvature (or a positive intermediate curvature in a suitable sense). We study the moduli space M^pos_*_(M× I)g of concordances of such metrics (with appropriate boundary conditions) which restrict to a given metric g on M × \0\ ∪∂ M × I. We show that π4*M^pos_*_(M × I)g ⊗ Q ≠ 0 in a stable range provided M is even. We obtain analogous results when positive scalar curvature is replaced by k-positive Ricci curvature for k ≥ 2.