Abstract
An imitation of the present cosmological constant by the slowly-rolling scalar field f (quintessence) requires an extreme fine tuning of the potential U( f), that is the problems appear related to the cosmological constant problem and flatness conditions. The field theory is presented which gives rise to the quintessence potential without any fine tuning in the very wide class of models. At the same time the models reproduce equations of Einstein's GR and allow for possibility of inflation in the very early universe.
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