DYNAMICAL SYSTEM ANALYSIS OF ANISOTROPIC AND HOMOGENOUS f(R) GRAVITY MODELS

Abstract

With the publication of Einstein's theory of general relativity, cosmology ceased to be an ideational field and turned into a serious field of study. Later, studies showed that it is more beneficial to modify general relativity. The first important motivation came from the search for a unified theory of all fundamental forces. But it is impossible to take the necessary steps without modifying the standard General Relativity. The latest motivations for modified gravities came from modern astrophysical and cosmological observations. One of the two important types of observation is the current matter-energy composition of the universe. The second observation is about the dark energy and the growing amount of evidence that the universe is now undergoing an accelerated expansion phase. Considering all these findings, it is clear that creating a picture for the evolution and the matter-energy content of the universe is challenging. The currently proposed cosmological model is the ΛCDM model which is mostly a phenomenological fit to the data, rather than a logical, unambiguous outcome. So, it is natural to modify general relativity to solve these problems, since in the context of standard general relativity it is much harder. So, we are interested in examining how does f(R) modification provides answers to some of the mentioned problems.