Generalized Einstein gravitational theory with vacuum vectorial field

In this paper a new generalized Einstein gravitational theory with four physical vacuum potentials and the Weyl connection is proposed. In the examined case of dust-like matter, differential equations of the second order for the vacuum potentials consistent with the proposed gravitational equations are obtained. A nonsingular cosmological solution for the homogeneous and isotropic physical vacuum and a vacuum cosmological influence on particles are found. Astronomical applications of this solution are discussed.