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

TL;DR

This paper explores homogeneous cosmological solutions within Weyl's scalar-tensor theory, analyzing anisotropic and isotropic models, but does not address cosmic acceleration or include scalar field potential.

Contribution

It provides new exact and qualitative solutions for homogeneous cosmologies in Weyl's scalar-tensor framework, expanding understanding of such models without scalar potential or cosmological constant.

Findings

Derived an anisotropic Kasner-type solution.

Obtained an analytical solution for flat isotropic model with stiff matter.

Performed qualitative analysis of solutions' behavior.

Abstract

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.