The variant of the quintessence theory is proposed in order to get an accelerated expansion of the Friedmannian Universe in the frameworks of relativistic theory of gravitation. The substance of quintessence is built up the scalar field of dark energy. It is shown, that function V(Phi), which factorising scalar field Lagrangian (Phi is a scalar field) has no influence on the evolution of the Universe. Some relations, allowing to find explicit dependence Phi on time, were found, provided given function V(Phi).
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