[en] It has been suggested recently to study the dynamics of a gravitating gluon condensate q in the context of a spatially flat Friedmann-Robertson-Walker universe. The expansion of the Universe (or, more generally, the presence of a nonvanishing Ricci curvature scalar R) perturbs the gluon condensate and may induce a nonanalytic term h-tilde(R,q) in the effective gravitational action. The aim of this article is to explore the cosmological implications of a particular nonanalytic term h-tilde∝η|R|^1/2|q|^3/4. With a quadratic approximation of the gravitating gluon-condensate vacuum energy density ρ_V(q) near the equilibrium value q₀ and a small coupling constant η of the modified-gravity term h-tilde, an 'accelerating universe' is obtained which resembles the present Universe, both qualitatively and quantitatively. The unknown component X of this model universe (here, primarily due to modified-gravity effects) has an effective equation-of-state parameter w_X which is found to evolve toward the value -1 from above.