  Borel's stability and vanishing theorem gives the stable cohomology of
$\mathrm{GL}(n,\mathbb{Z})$ with coefficients in algebraic
$\mathrm{GL}(n,\mathbb{Z})$-representations. By combining the Borel theorem
with the Hochschild-Serre spectral sequence, we compute the twisted first
cohomology of the automorphism group $\mathrm{Aut}(F_n)$ of the free group
$F_n$ of rank $n$. We also study the stable rational cohomology of the
IA-automorphism group $\mathrm{IA}_n$ of $F_n$. We propose a conjectural
algebraic structure of the stable rational cohomology of $\mathrm{IA}_n$, and
consider some relations to known results and conjectures. We also consider a
conjectural structure of the stable rational cohomology of the Torelli groups
of surfaces.
