  We prove the macroscopic cousins of three conjectures: 1) a conjectural bound
of the simplicial volume of a Riemannian manifold in the presence of a lower
scalar curvature bound, 2) the conjecture that rationally essential manifolds
do not admit metrics of positive scalar curvature, 3) a conjectural bound of
$L^2$-Betti numbers of aspherical Riemannian manifolds in the presence of a
lower scalar curvature bound. The macroscopic cousin is the statement one
obtains by replacing a lower scalar curvature bound by an upper bound on the
volumes of $1$-balls in the universal cover.
