Teorias f(R) de gravidade na formulação de Palatini
In this dissertation, after a brief review on the Einstein s General Relativity Theory and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models, we present and discuss the alternative theories of gravity dubbed f(R) gravity. These theories come about when one subs...
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| Formato: | Dissertação |
| Idioma: | por |
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Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/18587 |
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| Resumo: | In this dissertation, after a brief review on the Einstein s General Relativity Theory
and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological
models, we present and discuss the alternative theories of gravity dubbed
f(R) gravity. These theories come about when one substitute in the Einstein-Hilbert
action the Ricci curvature R by some well behaved nonlinear function f(R). They
provide an alternative way to explain the current cosmic acceleration with no need
of invoking neither a dark energy component, nor the existence of extra spatial dimensions.
In dealing with f(R) gravity, two different variational approaches may
be followed, namely the metric and the Palatini formalisms, which lead to very
different equations of motion. We briefly describe the metric formalism and then
concentrate on the Palatini variational approach to the gravity action. We make a
systematic and detailed derivation of the field equations for Palatini f(R) gravity,
which generalize the Einsteins equations of General Relativity, and obtain also the
generalized Friedmann equations, which can be used for cosmological tests. As an
example, using recent compilations of type Ia Supernovae observations, we show
how the f(R) = R − fi/Rn class of gravity theories explain the recent observed
acceleration of the universe by placing reasonable constraints on the free parameters
fi and n.
We also examine the question as to whether Palatini f(R) gravity theories
permit space-times in which causality, a fundamental issue in any physical theory
[22], is violated. As is well known, in General Relativity there are solutions to the
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field equations that have causal anomalies in the form of closed time-like curves,
the renowned Gödel model being the best known example of such a solution. Here
we show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with
density and pressure p that satisfy the weak energy condition + p 0 is necessarily
isometric to the Gödel geometry, demonstrating, therefore, that these theories
present causal anomalies in the form of closed time-like curves. This result extends a
theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We
derive an expression for a critical radius rc (beyond which causality is violated) for
an arbitrary Palatini f(R) theory. The expression makes apparent that the violation
of causality depends on the form of f(R) and on the matter content components.
We concretely examine the Gödel-type perfect-fluid solutions in the f(R) =
R−fi/Rn class of Palatini gravity theories, and show that for positive matter density
and for fi and n in the range permitted by the observations, these theories do not
admit the Gödel geometry as a perfect-fluid solution of its field equations. In this
sense, f(R) gravity theory remedies the causal pathology in the form of closed timelike
curves which is allowed in General Relativity. We also examine the violation
of causality of Gödel-type by considering a single scalar field as the matter content.
For this source, we show that Palatini f(R) gravity gives rise to a unique Gödeltype
solution with no violation of causality. Finally, we show that by combining a
perfect fluid plus a scalar field as sources of Gödel-type geometries, we obtain both
solutions in the form of closed time-like curves, as well as solutions with no violation
of causality |
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