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Previous issue date: 2017-03-24 === Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) === A evid?ncia observacional da expans?o acelerada do Universo tem sido a principal raz?o
para uma revis?o da evolu??o cosmol?gica como previsto pela Relatividade Geral
(RG). Atualmente existe duas principais abordagens para resolver este problema: pela
introdu??o nas equa??es de Einstein de um termo o qual representa um novo tipo de
fluido (a chamada energia escura) possuindo caracter?sticas ex?ticas ou pela modifica??o
da teoria de gravita??o. Nesta tese n?s focamos na segunda abordagem, particularmente,
as teorias conhecidas como teorias f(R) de gravidade as quais t?m recebido muita aten??o
nos ?ltimos anos. Neste contexto, a equa??o de Raychaudhuri permite examinar a
estrutura do espa?o-tempo como um todo sem solu??es espec?ficas das equa??es de Einstein,
desempenhando assim um papel central para a compreens?o da atra??o gravitacional
em Astrof?sica e Cosmologia. Na teoria da Relatividade Geral sem uma constante
cosmol?gica, uma contribui??o n?o-positiva da geometria do espa?o-tempo a equa??o de
Raychaudhuri ? usualmente interpretada como a manifesta??o do car?ter atrativo da gravidade.
Neste caso, condi??es de energia espec?ficas - de fato a condi??o de energia forte
- deve ser assumida, a fim de garantir o car?cter atrativo. No contexto das teorias f(R)
de gravidade, no entanto, mesmo assumindo as condi??es de energia usuais pode-se ter
uma contribui??o positiva para a equa??o de Raychaudhuri. Al?m de nos fornecer uma
maneira simples de explicar a observada expans?o acelerada do Universo, este fato abre a
possibilidade de um car?ter repulsivo deste tipo de gravidade. Nesta tese n?s abordamos
o car?cter atrativo/n?o-atrativo da gravidade f(R) ? luz da equa??o de Raychaudhuri e
fazemos uso da condi??o de energia forte, juntamente com estimativas recentes dos par?metros
cosmogr?ficos, para colocar limites em uma classe paradigm?tica de teorias f(R)
de gravidade. === 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.
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