  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.
