Defeitos analíticos em gravidade f(R).

Abstract

Defects are solutions derived from non-linear differential equations and they are present within the framework of classical field theory. These solutions can be compared with solitary waves, which are classificated as stable, or kinks in one dimension, or instable, called lumps in one dimension. This dissertation aims to introduce an application of topological defects in cosmological model based on a modificated gravity theory. This theory, alternative to general relativity, searches to generalize it in order to explain phenomena not described in usual Einstein equations. The f(R) theory is an example of such alternative theory and it is based on the addition of a geometric higher order term in the Einstein-Hilbert action. In this dissertation we worked with the so-called Starobinski’s model for f(R), via a method called fisrt-order formalism. Such a method consists in connect a function of a background scalar field with Hubble’s parameter. As new results, we derived analytical cosmological parameters like the equation of state (EoS) parameter, the deceleration parameter, amoung others. These parameters are able to describe the actual expansion phase of the universe.