Based on the requirement that the gauge invariance principle for the Poincaré-Weyl group be satisfied for the space-time manifold, we construct a model of space-time with the geometric structure of a WeylCartan space. We show that three types of fields must then be introduced as the gauge ("compensating") fields: Lorentz, translational, and dilatational. Tetrad coefficients then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincaré-Weyl group.

The variational procedure for the nonlinear Langrangians is investigated for a tetrad description of an affine metric space. The equations of the gravitation field with a source in the form of matter with a dilatational charge are derived for the general Langrangian quadratically dependent on the curvature, torsion, and nonmetricity tensors. It is established that differential variational identities hold true for these equations.

At the present time, the "Gravity Probe B" (GP-B) experiment is being performed on the orbit aimed at investigation into features of motion of a rotating probe body (gyro) in the Earth's gravitational field. The results of measurements are under processing and will be compared with the predictions of GRT and its various generalizations.It is well known that classical experiments confirm GRT accurate to 0.3%. Therefore, there is reason to hope that the foregoing experiment will identify departures from GRT.In [1], it is proposed to treat possible variations of the experiment results from the GRT predictions as the presence of torsion of spacetime in the above experiment. In this work, it is assumed that a gyro could respond to torsion if a rotating planet-type body was able to produce spacetime torsion, hence the experiments with a gyro like the above GRB can be the best means for determination of the most adequate of all possible unconventional gravitation theories allowing for torsion.A nonconventional theory is necessitated by the fact that it is assumed in the conventional Poincaré -gauge gravitation theory [2, 3] that the orbital angular momentum cannot be a source of field due to the absence of translational invariance of the field equations arising in this case. This was discussed in detail in the well-known review [3]. In [1], this opinion was cited as a common folklore in modern theory of gravitational field. This difficulty was overcome in a new variant of the Poincaré-gauge gravitation theory [4, 5] and a recently developed Poincaré-Weyl-gauge gravitation theory [6, 7], where the angular momentum a m M along with the spin moment a m S occur as a source of gravitational field, including the torsional field, without violation of translational invariance of the field equations.The theory is developed on the basis of the Noether theorems allowing gauge fields dynamically realizing the laws of conservation of energy-momentum, total rotational moment (orbital and spin), and dilatation charge to be introduced. The dilatation charge is due to the invariance of the theory with respect to tension and compression of spacetime. As a result, the theory necessitates the Weyl-Kartan geometry with curvature, torsion, and nonmetricity of the Weyl type in spacetime.Within this approach, the tetrads a h μ are not true gauge fields, they represent certain functions of the introduced gauge fields: Lorentzian m a A (rotational r-field), translational k a A (t-field), and dilatational a A (d-field). An equation for the gauge field m a A is as follows:

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 , = , = ,

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