The problem of a cosmological constant within the conformal gravitation theory in the Weyl–Kartan space

Abstract

Кeywords: conformal gravitation theory, scalar field, Weyl-Kartan space, physical vacuum, dark energy.According to the quantum theory calculations, the cosmological constant responsible for accelerated expansion of the Universe must differ by 120 orders of magnitude at the early and modern stages of evolution of the Universe. In this work, this dynamics of cosmological constant is accounted for.The Poincaré-Weyl gauge gravitation theory developed in [2] is the basis for further constructions [1]. This theory is invariant with respect to both the Poincaré subgroup and the Weyl subgroup -extensions and compressions (dilatations) of spacetime. In the theory, there occurs an additional scalar field ( ) x β introduced by Dirac. Its transformation under dilatations can be described asThis results in the theory invariance with respect to conformal transformations = 0 , = 2 , = , = ,

Spherically symmetric solution of the Weyl-Dirac theory of gravitation and possible influence of dark matter on the interplanetary spacecraft motion

“…On the basis of PWTG, the conformal theory of gravitation in Cartan-Weyl spacetime with Dirac scalar has been developed [15,16,17,18] with the Lagrangian density 4-form (in exterior form formalism) [20,21],…”

“…Further on the basis of the given result the theory of gravitation in a Cartan-Weyl space was constructed [15,16,17,18], which generalizes the Einstein-Cartan and the Poincar'e gauge theories of gravitation on presence of nonmetricity of the Weyl's type and uses the Dirac scalar field for supporting conformance of the theory. This generalized theory of gravitation is pertinent to name the Weyl-Dirac theory of gravitation.…”

Approximate axially symmetric solution of the Weyl-Dirac theory of gravitation and the spiral galactic rotation problem

“…On the base of this theory the new conformal Weyl-Dirac theory of gravitation is proposed, which is the gravitational theory in Cartan-Weyl spacetime with the additional geometrical structure as a Dirac scalar field, 4 representing the dark matter model. [5][6][7] The post-Riemannian Cartan-Weyl space has geometrical properties of curvature, torsion, and nonmetricity of the Weyl's type, in which a Weyl 1-form is defined by the gradient of the Dirac scalar field β. The resulting theory of gravita-tion has been named by Weyl-Dirac theory of gravitation, since it generalizes the Einstein-Cartan theory of gravitation to include nonmetricity of the Weyl's type in the Cartan-Weyl space with the additional Dirac scalar field.…”