Dark energy as a cosmological consequence of existence of the Dirac scalar field

The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (describing by an effective cosmological constant) is a function of the Dirac scalar field $\beta$. This solution describes the exponential decreasing of $\beta$ at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.