  Equations of the conformal theory of gravity with a Dirac scalar field in a
Weyl-Cartan space-time have been derived. An exact solution of the equation for
a scalar field, which has kind of a decreasing exponential function, has been
found. This allows to explain a significant decrease (during of the period of
inflation) the energy of physical vacuum (dark energy), which has been
identified with the energy of the Dirac scalar field.
