On cosmological corrections to the equations of general relativity based on Weyl’s principle of scale invariance

Generalizations of the Einstein gravitational and Maxwell electromagnetic field equations are proposed which are based on Weyl’s principle of scale invariance and contain Weyl’s vector field with four components. The Weyl field is regarded as a weak one giving small corrections to the Einstein and Maxwell field equations but playing an important role in cosmological processes. The proposed system of field equations is applied to a homogeneous and isotropic vacuum and a nonsingular cosmological solution to them is found. This solution is used to describe the influence of the Weyl field on propagating electromagnetic waves and moving free particles in vacuum. The result is a new cosmological model that helps explain the nature of dark matter and interpret intriguing data on ancient galaxies obtained by the James Webb Space Telescope.