A equação de Raychaudhuri e o caráter não-atrativo da gravidade f(R)

Abstract

The observational evidence of the accelerated expansion of the Universe has been the main reason for a revision of the cosmological evolution as predicted by General Relativity (GR). Currently there are two main approaches to solving this problem: by introducing in the Einstein’s equations a term which represent a new kind of fluid (the so-called dark energy possessing exotic features) or by the modification of the gravitation theory. In this thesis we focus on the second approach, particularly the theories know as f(R) theories of gravity, which have received many attention in the last years. In this framework, the Raychaudhuri equation makes possible to examine the whole of spacetime structures without specific solutions of Einstein’s equations, playing so a central role to the understanding of gravitational attraction in Astrophysics and Cosmology. In the general relativity theory of gravity without a cosmological constant, a non-positive contribution from the spacetime to Raychaudhuri’s equation is usually interpreted as manifestation of the attractive character of gravity. In this case, particular energy conditions - indeed the strong energy condition - must be assumed in order to guarantee this attractive character. In the context of f(R) theories of gravity however, even assuming the usual energy conditions we may have a positive contribution to Raychaudhuri’s equation. Besides giving us a simple way to explain the observed accelerated expansion of the Universe, this fact opens the possibility of a repulsive character of this kind of gravity. In this thesis we address the attractive/non-attractive character of f(R) theories of gravity at the light of Raychaudhuri’s equation and make use of the strong energy condition, jointly with recent estimated values for the cosmographic parameters, in order to put bounds on a paradigmatic class of f(R) theories of gravity.