  We provide an isoperimetric comparison theorem for small volumes in an
$n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as
in Definition $2.3$, involving the scalar curvature function. Namely in strong
bounded geometry, if the supremum of scalar curvature function $S_g<n(n-1)k_0$
for some $k_0\in\mathbb{R}$, then for small volumes the isoperimetric profile
of $(M^n,g)$ is less then or equal to the isoperimetric profile of
$\mathbb{M}^n_{k_0}$ the complete simply connected space form of constant
sectional curvature $k_0$. This work generalizes Theorem $2$ of [Dru02b] in
which the same result was proved in the case where $(M^n, g)$ is assumed to be
just compact. As a consequence of our result we give an asymptotic expansion in
Puiseux's series up to the second nontrivial term of the isoperimetric profile
function for small volumes. Finally, as a corollary of our isoperimetric
comparison result, it is shown, in the special case of manifolds with strong
bounded geometry, and $S_g<n(n-1)k_0$ that for small volumes the
Aubin-Cartan-Hadamard's Conjecture in any dimension $n$ is true.
