Abstract
A new mechanism of adjustment of vacuum energy down to the observed value from an initially huge one is considered. The mechanism is based on a very strong variation of the gravitational coupling constant in the very early universe. The model predicts that the noncompensated remnant of vacuum energy changes very slowly at late stages of the cosmological evolution and is naturally close to the observed one. Asymptotically the effective vacuum energy tends to a negative value, so the cosmological expansion should stop and turn into contraction. There remains the problem of introduction of the usual matter into the model and therefore realizing realistic cosmology.
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