On a Generalization of the Equations of General Relativity Based on Weyl’s Principle of Scale Invariance

Generalizations of the Einstein gravitational and Maxwell electromagnetic field equations are studied, which are based on Weyl’s principle of scale invariance and contain Weyl’s vector field with four components. In these generalizations, the results obtained in our earlier publication (Grav. Cosmol. 25, 237–242 (2019)) are used and substantially developed. The Weyl field is regarded as a weak one, which gives small corrections to the Einstein and Maxwell field equations but could play an important role in cosmological processes. The considered equations are examined for an arbitrary system of particles interacting by means of gravitational and electromagnetic forces. The conditions of consistency of these equations are studied, which result in four second-order differential equations for four components of Weyl’s vector. The proposed system of field equations is applied to a homogeneous and isotropic vacuum, and a nonsingular cosmological solution is obtained. This solution is applied to describe the influence of the Weyl field on propagating electromagnetic waves and moving free particles in vacuum. Cosmological aspects of the obtained results are discussed.