Dark energy, Dirac's scalar field and the cosmological constant problem
  The solutions of the field equations of the conformal theory of gravitation
with Dirac scalar field in Weyl-Cartan spacetime in very early universe are
obtained. In this theory dark energy (describing by an effective cosmological
constant) is a function of the Dirac scalar field $\beta$. These solutions
describe the exponential decreasing of $\beta$ at the first exponential stage
of inflation. One of these solutions has a limit to a constant value of the
dark energy at large time that can give a way to solving the fundamental
cosmological constant problem as a consequence of the fields dynamics in the
early universe.
