Modelos cosmológicos inflacionários tipo Starobinsky

Abstract

In this work we study the Early Universe. Over the past years cosmological inflation has become an essential ingredient of any model which aims at describing the universe in its primordial stage. The predictions of inflationary models can be related to measurements of the Cosmic Microwave Background (CMB) and then, these results have allowed the proposed models to be rigorously tested. In this dissertation, we present the Cosmological Standard Model and analyze some problems as motivation to introduce the concept of cosmological inflation. We describe the inflationary paradigm in terms of a scalar field, find their dynamic equations and use the slow-roll approximation, which allowed us to calculate the spectral indices ns and r of two inflationary models. We have analyzed the theory f(R) in an inflationary context and discuss Starobinsky’s model. It was possible to calculate the spectral indices for this model, too. By the analysis of dynamical systems, we were able to propose an exponential correction to Starobinsky’s model.