On negatively curved bundles with hyperbolic fibers outside the Igusa stable range

We prove that the Teichm"{u}ller space ${\mathcal{T}}^{<0}(M)$ of negatively curved metrics on a hyperbolic manifold $M$ has nontrivial $i$-th rational homotopy groups for some $i>\dim M$. Moreover, some elements of infinite order in ${\pi }_{i}BDiff(M)$ can be represented by bundles over $S^i$ with fiberwise negatively curved metrics.