Gravitação Invariante de Weyl: teoria e aplicações

Abstract

The present thesis is dedicated to the study of the Weyl Invariant Gravitational Theory, a modification and reinterpretation of the original theory proposed by Hermann Weyl. Initially,

we present in detail the construction of Weyl’s theory. Next, we develop a gauge-invariant for- mulation for the unified theory of Weyl. This formulation consists of a proposal that renders

both the metric tensor and the Weyl field invariant quantities under gauge transformations. With this, it is possible to construct a gauge-invariant proper time definition, in addition to allowing the description of the coupling between geometric fields and matter. In this way, we obtain a new alternative theory of gravitation. An important aspect emphasized in the thesis is that the Weyl geometric 1-form can be formally interpreted as a massive vector field, which refers us to the theory proposed in 1936 by the Romanian physicist Alexandru Proca, who aimed to describe the interaction and dynamics of massive spin-1 bosons. As an application of the field equations of the Weyl invariant theory, we investigate a solution in the weak-field regime. Furthermore, we study in detail the propagation of gravitational waves in this new modified theory of gravity. Finally, we propose an alternative approach to the problem of the origin of dark matter. We show that, for appropriate values of the free parameter of the adopted model, the Weyl field, during the matter-dominated, era, exhibits the expected behavior for a dark matter candidate.