Homogeneous Cosmological Models in Weyl's Geometrical Scalar-Tensor Theory

In this paper, we consider homogeneous cosmological solutions in the context of the Weyl geometrical scalar-tensor theory. Firstly, we exhibit an anisotropic Kasner type solution taking advantage of some similarities between this theory and the Brans-Dicke theory. Next, we consider an isotropic model with a flat spatial section sourced by matter configurations described by a perfect fluid. In this model, we obtain an analytical solution for the stiff matter case. For other cases, we carry out a complete qualitative analysis theory to investigate the general behaviour of the solutions, presenting some possible scenarios. In this work, we do not consider the presence of the cosmological constant nor do we take any potential of the scalar field into account. Because of this, we do not find any solution describing the acceleration of the universe.

Automated summary

In this paper, homogeneous cosmological solutions within the framework of Weyl geometrical scalar-tensor theory are investigated. An anisotropic Kasner type solution is first presented by exploiting similarities with the Brans-Dicke theory. An isotropic model with a flat spatial section sourced by a perfect fluid is then considered, where an analytical solution for the stiff matter case is obtained. For other cases, a complete qualitative analysis is performed to explore the general behavior of the solutions and propose potential scenarios. The absence of the cosmological constant and scalar field potential prevents the discovery of any solution describing the acceleration of the universe.