  We study inflationary cosmology and the late-time accelerated expansion of
the universe in non-minimal Yang-Mills (YM) theory, in which the YM field
couples to a function of the scalar curvature. It is shown that power-law
inflation can be realized due to the non-minimal YM field-gravitational
coupling which maybe caused by quantum corrections. Moreover, it is
demonstrated that both inflation and the late-time accelerated expansion of the
universe can be realized in a modified YM-$F(R)$ gravity which is consistent
with solar system tests. Furthermore, it is shown that this result can be
realized also in a non-minimal vector-$F(R)$ gravity. In addition, we consider
the duality of the non-minimal electromagnetic theory and that of the
non-minimal YM theory, and also discuss the cosmological reconstruction of the
YM theory.
