We suggest one of the possible ways to compensate the large negative quantum-topological QCD contribution to the vacuum energy density of the Universe by means of a positive constant contribution from a cosmological Yang-Mills field. An important role of the exact particular solution for the Yang-Mills field corresponding to the finite-time instantons is discussed. An interesting connection of the compensation mechanism to the color confinement in the framework of instanton models has been pointed out. Besides the scale, this proposal relies on one yet free dimensionless normalisation constant which cannot be fixed by the perturbative QCD theory, and thus should be fine-tuned for the exact compensation to hold.

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