On macroscopic dimension of rationally inessential manifolds

We show that, for a rationally inessential orientable closed $n$-manifold $M$ whose fundamental group is a duality group, the macroscopic dimension of its universal cover $\widetilde{M}$ is strictly less than $n$: $\dim_{MC}\widetilde{M}<n$. As a corollary, we obtain the following partial result towards Gromov's conjecture:
\textit{The inequality $\dim_{MC}\widetilde{M}<n$ holds for the universal cover $\widetilde{M}$ of a closed spin $n$-manifold $M$ with a positive scalar curvature metric if the fundamental group $\pi_1(M)$ is a duality group satisfying the analytic Novikov conjecture.}