Gravitation theory with a Dirac scalar field in the exterior form formalism and the cosmological constant problem

As a consequence of the Poincare-Weyl gauge theory of gravity, the space-time possesses the geometric structure of Cartan-Weyl CW ₄ space with curvature and torsion 2-forms and a Weyltype nonmetricity 1-form. The Dirac field ??(x) appears as an essential additional geometric component with respect to the metric tensor. The conformal theory of gravity coupled with ??(x) in the exterior form formalism is considered. At an early stage of the universe evolution, we consider these field equations for the spatially flat FRWmetric, assuming the densities of ordinarymatter and dark matter to be very small. Then the field equations can be expressed in terms of the metric tensor and ??(t) only and have an exponentially diminishing solution for ??(t), which can explain an exponential decrease of dark energy (the energy of physical vacuum) as a function of time as a consequence of field dynamics in the ultra-early Universe.