Diffeomorphisms and positive curvature

We prove the existence of elements of infinite order in the homotopy groups of the spaces ${\mathcal{R}}_{Ric>0}(M)$ and ${\mathcal{R}}_{sec>0}(M)$ of positive Ricci and positive sectional curvature, provided that $M$ is high-dimensional and Spin, admits such a metric and has a non-vanishing rational Pontryagin class.