Inflação em modelos de gravidade generalizada: análise dinâmica e singularidades

Abstract

The concept of inflation was firstly introduced in order to solve some problems that the original Big Bang cosmology could not explain such as the flatness and the horizon problems. In the inflationary phase, the Universe undergoes an accelerating expansion (a > 0) for a short time during which there is the production of the density perturbations that are responsible for the formation of the large scale structures in the Universe. The simplest cosmological models found in the literature are governed by a scalar field φ, called inflaton, minimally coupled to the Einstein gravity and subjected to a self-interaction potential V (φ). The crucial ingredient of the inflation is its slow time evolution (slow roll) in which the self-interaction potential V (φ) overcomes the kinetic energy term φ/2 and produces this accelerating expansion. In this thesis, we consider a generalized Lagrangian given by f(R, φ,X) to study cosmological models, mainly in their inflationary phases. This Lagrangian comprehends any type of gravity theory found in the literature such as the minimal coupling gravity (i.e. quintessence, phantom energy, k-inflation or k-essence models) and the scalar-tensor gravity such as Brans-Dicke, non-minimal coupling and modified gravity models. We are specially interested in describing the types of singularities that can be found in anisotropic and homogeneous cosmological models in which the Lagrangian assumes the particular form f(R, φ,X) = f(R, φ) + p(φ,X), where f(R, φ) represents the non-minimal coupling term and p(φ,X) is the non-canonical kinetic term. The study of these singularities stablishes many constraints for the viability of cosmological models presenting a generalized gravity Lagrangian.