Quintessence scalar field in the relativistic theory of gravity

We propose a variant of the quintessence theory in order to obtain an accelerated expansion of the Friedmann universe in the framework of the relativistic theory of gravity. The scalar field of dark energy creates the substance of quintessence. We show that the function $V(\Phi)$ that factors the Lagrangian of the scalar field $\Phi$ does not influence the evolution of the universe. We find some relations that allow finding the explicit time-dependence of $\Phi$ if only the function $V(\Phi)$ is chosen.