The so-called 'cosmic web', comprising cosmic voids and galaxy clusters, has been proven to be extremely sensitive to deviations from General Relativity. This could be further investigated by future large-scale surveys, such as with the European Space Agency satellite Euclid. In this study, the parameter |fR0| from f(R) gravity is constrained by considering the Euclid survey specications to predict the observed numbers of voids and clusters in bins of redshift, mass and, only for voids, density contrast. From these values, the Fisher matrix is computed for three values of |fR0|, 10-4, 10-6 and 10-8, by assuming a flat Universe with a component that mimics the cosmological constant. The probability density functions are obtained for |fR0| and seven other parameters from the fiducial model considered (ns, h, Ωb, Ωm, σ8, w0 and wa).

No description available.

Gravitation is the dominant influence in most astrophysical interactions. Weak-field interactions have been extensively studied, but the strong-field regime remains largely unexplored. Gravitational waves (GWs) are an excellent means of accessing strong-field regions. We investigate what we can learn about both astrophysics and gravitation from strong-field tests and, in particular, GWs; we focus upon extreme-mass-ratio (EMR) systems where a small body orbits a much more massive one. EMR bursts, a particular class of GW signals, could be used to determine the properties of massive black holes (MBHs). They could be detectable with a space-borne interferometer from many nearby galaxies, as well as the Galactic centre. Bursts could provide insightful constraints on the MBHs' parameters. These could elucidate the formation history of the MBHs and, by association, their host galaxies. The Galactic centre is the most promising source. Its event rate is determined by the stellar distribution surrounding the MBH; the rate is not high, but we still expect to gain useful astronomical information from bursts. Strong-field tests may reveal deviations from general relativity (GR). We calculate modifications that could be observed assuming metric f(R)-gravity as an effective alternative theory. Gravitational radiation is modified, as are planetary precession rates. Both give a means of testing GR. However, existing laboratory measurements already place tighter constraints on f(R)-gravity, unless there exists a screening effect, such as the chameleon mechanism, which suppresses modifications on small scales. To make precision measurements of astrophysical systems or place exacting bounds on deviations from GR, we must have accurate GW templates. Transient resonances are currently not included in the prescription for generating EMR inspiral waveforms. Their effects can be estimated from asymptotic expansions of the evolving orbital parameters. The quantitative impact on parameter estimation has yet to be calculated, but it appears that it shall be necessary to incorporate resonances when creating inspiral waveforms.

We employ observational data about the largest cosmic void and most massive galaxy cluster known to date, the 'Cold Spot' void and the 'El Gordo' cluster, in order to constrain the parameter |fR0| from the f(R) gravity formulation by Hu and Sawicki and the matter power spectrum normalization at present time, σ8. We obtain the marginalized posterior distribution for these two parameters through a Markov Chain Monte Carlo analysis, where the likelihood function is modeled through extreme value statistics. The prior distribution for the additional cosmological parameters included in the computations (Ωdmh2, Ωbh2, h and ns) is matched to recent constraints. By combining the likelihood functions for both voids and clusters, we obtain a mean value log|fR0| = -5.1 ± 1.6, which is compatible with General Relativity (log|fR0| ≤-8) at 95% confidence level, but suggests a preference for a non-negligible modified gravity correction.

Made available in DSpace on 2015-03-03T15:15:24Z (GMT). No. of bitstreams: 1 ThiagoBRFO_DISSERT.pdf: 776732 bytes, checksum: 79a4002c3c2d724d3d1651680816802b (MD5) Previous issue date: 2010-07-01 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / 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 viii field equations that have causal anomalies in the form of closed time-like curves, the renowned G?del model being the best known example of such a solution. Here we show that every perfect-fluid G?del-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 G?del geometry, demonstrating, therefore, that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on G?del-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 G?del-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 G?del 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 G?del-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 G?deltype solution with no violation of causality. Finally, we show that by combining a perfect fluid plus a scalar field as sources of G?del-type geometries, we obtain both solutions in the form of closed time-like curves, as well as solutions with no violation of causality / Nesta disserta??o, ap?s uma breve revis?o sobre a Teoria da Relatividade Geral de Einstein e suas aplica??es para os modelos cosmol?gicos de Friedmann-Lemaitre- Robertson-Walker (FLRW), apresentamos e discutimos as teorias alternativas de gravidade denominadas de gravidade f(R). Estas teorias surgem quando substitu?mos na a??o de Einstein-Hilbert o escalar de curvatura de Ricci R por qualquer fun??o f(R) n?o-linear bem comportada. Elas fornecem uma maneira alternativa para explicar a acelera??o c?smica atual sem necessitar envolver qualquer componente de energia escura ou a exist?ncia de dimens?es espaciais extras. Quando lidamos com gravidade f(R), dois diferentes princ?pios variacionais podem ser seguidos, a saber, o formalismo m?trico e o de Palatini, os quais levam a equa??es de movimento muito diferentes. Descrevemos brevemente o formalismo m?trico e ent?o nos concentramos no princ?pio variacional de Palatini para a a??o da gravidade. Fazemos uma deriva??o sistem?tica e detalhada das equa??es de campo para a gravidade f(R) de Palatini, as quais generalizam as equa??es de Einstein da Relatividade Geral. Em seguida obtemos as equa??es de Friedmann generalizadas, que podem ser usadas para testes cosmol?gicos. Para exemplificar, usamos compila??es recentes de observa??es de supernovas do tipo Ia e mostramos como a classe de teorias de gravidade f(R) = R ? /Rn explica a recente acelera??o observada do universo quando colocamos v?nculos razo?veis sobre os par?metros livres e n. Examinamos tamb?m a quest?o de como teorias f(R) de gravidade em Palatini permitem espa?os-tempos em que a causalidade, um resultado fundamental em qualquer teoria f?sica [22], ? violada. Como ? bem conhecido, na Relatividade Geral existem solu??es para as equa??es de campo que possuem anomalias causais na forma de curvas tipo-tempo fechadas, sendo o modelo de G?del o exemplo mais bem conhecido de tais solu??es. Aqui mostramos que toda solu??o do tipo-G?del de gravidade f(R) em Palatini com fluido perfeito, caracterizado por densidade e press?o p, satisfazendo a condi??o de energia fraca + p 0, ? necessariamente isom?trica ? geometria de G?del, demonstrando, portanto, que essas teorias apresentam anomalias causais na forma de curvas tipo-tempo fechadas. Esses resultados ampliam um teorema sobre modelos tipo-G?del para a estrutura das teorias de gravidade f(R) de Palatini. Derivamos uma express?o para o raio cr?tico rc (al?m do qual a causalidade ? violada) para uma teoria arbitr?ria de gravidade f(R) de Palatini. A express?o encontrada tornou claro que a viola??o da causalidade depende da forma de f(R) e dos componentes do conte?do de mat?ria. Examinamos objetivamente as solu??es tipo-G?del de um fluido perfeito na classe f(R) = R ? /Rn das teorias de gravidade de Palatini e mostramos que, para uma densidade de mat?ria positiva e para e n em um intervalo permitido pelas observa??es, essas teorias n?o admitem como solu??es de suas equa??es de campo a geometria de G?del juntamente com um fluido perfeito. Nesse sentido, teorias de gravidade f(R) remediam a patologia causal na forma de curvas tipotempo fechadas que ? permitido na Relatividade Geral. Examinamos tamb?m essa viola??o de causalidade ao considerar um campo escalar como conte?do material. Para essa fonte, mostramos que a gravidade f(R) em Palatini d? origem a uma ?nica solu??o do tipo-G?del sem viola??o de causalidade. Finalmente, mostramos que a combina??o de um fluido perfeito mais um campo escalar como fontes de geometrias tipo-G?del, levam a solu??es na forma de curvas tipo-tempo fechadas como a solu??es sem viola??o de causalidade

Cette thèse est composée de deux parties qui sont relativement indépendantes l’un de l’autre. Dans la première partie,une autre théorie de la gravitation que l’on appelle la gravité de f(R), est étudiée. Une première analyse mathématique est discutée sur cette théorie, y compris la formulation mathématique du problème de Cauchy, la discussion sur le choix du couplage, et la formulation mathématique des équations différentielles. Ce système des équations différentielles est de quatrième ordre et très impliqué. Pour pouvoir établir l’existence locale, une série de transformations et reformulation et introduites. Elles nous amènent à une formulation que l’on l’appelle la formulation conforme augmenté. Avec cette formulation, l’existence locale est établie. La deuxième partie est consacrée à l’analyse d’un type de système non-linéaire composé des équations d’onde et équations de Klein-Gordon. Ce type de système apparaît naturellement dans de nombreux modèles physiques: le plus important, l’équation d’Einstein couplé avec un champ scalaire réel du massif et le système de la formulation conforme augmentée de la théorie de f(R). La difficulté principale est le manque de la symétrie: un des champs de vecteur de Killing conforme de l’opérateur d’onde, le champ de vecteur de scaling S := t∂ t +r∂ r, n’est pas un champ de vecteur de Killing conforme de l’opérateur de Klein Gordon. Pour franchir cette difficulté, un nouveau cadre, appelé la méthode de feuilletage hyperboloïdal, est introduit. Avec ce cadre, nous pouvons encadrer les équations d’onde et les équations de Klein-Gordon dans le même cadre. Cela nous permet d’établir un résultat d’existence globale pour les données initiales petites et localisées dans un compact. / This these is composed by two parts which are relatively independent to each other. In the first part an alternative theory of the gravitation, the so-called f(R) gravity, is studied. A first mathematical analysis is discussed on this theory, including the mathematical formulation of the Cauchy problem, the discussion on the choice of coupling, the mathematical formulation of the differential system. This system is four-order and highly involved. To establish the local well-posedness result, a series of transformations ans re-formulations is introduced and we finally arrived at a formulation, called the augmented conformal formulation with which we have managed to establish the local well-poseness theory.The second part is devoted to the analysis of a type of coupled wave and Klein-Gordon system. This kind of system arises naturally in many physical model, especially in the Einstein equation coupled with a real massive scalar field and the augmented conformal formulation of the f(R) gravity. The main difficulty to treat this type of system is the lack of symmetry: one of the conformal Killing vector filed of the linear wave operator, the scaling vector field S := t∂t+r∂r is not a conformal Killing vector field of the linear Klein-Gordon operator. To overpass this difficult, a new framework, called the hyperboloidal foliation method is introduced. With this framework we can encompass the wave equations and the Klein-Gordon equations in the same framework. This allowed us to establish a global well-posedness result for compactly supported, small amplitude initial data.