Modelo cosmológico no formalismo covariante de escala

Abstract

The present work deals with the possibility that two systems of units, which describe different eras during the evolution of the universe, can be related through a timescale transformation, being this transformation responsible for mapping different eras of the universe. The gravitational unit system describes gravity in the current era, governed by general relativity, and the atomic unit system describes a primordial universe, with a modified gravitation. The model was proposed by Canuto et. al., and brings as a consequence the temporal variation of the gravitational constant 𝐺, this concept being in agreement with Dirac large number hypothesis, and also with general relativity. As a particular case, keeping 𝐺 constant means dealing with equations in gravitational units, whereas the temporal variation of 𝐺 can lead to a system of modified field equations in atomic units, which describe the universe in an era in the past. In order to obtain cosmological solutions with the proposed formalism, different possibilities of cosmological constituents for its application were analyzed, namely, the generalized Chaplygin fluid, the generalized and complete Van der Waals fluid and the barotropic fluid, as well as different possibilities for the mathematical function responsible for the transformation between systems of units. The results found show a different behavior for the scale factor when comparing the systems of gravitational and atomic units after the transformation is applied. A decelerated-accelerated behavior is observed for the scale factor in gravitational units, and a de Sitter behavior in atomic units, results in agreement with the standard model of cosmology.