Theory of gravity admitting arbitrary choice of the energy density reference level

Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class of vector fields unlike the General Relativity (GR), where they are arbitrary. The possible cosmological implication of the model proposed is that the residual vacuum fluctuations dominate during the whole evolution of the universe. That resembles the universe having a nearly linear dependence of scale factor on cosmic time.