2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203188We 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.21 pages, no figure, shortened version, accepted in PRD, misprints correctedHigh Energy Physics - TheoryAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Phenomenologytext