Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

A Generalization of Gravity

I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to Cayley's hyperdeterminants. The resulting diff-invariant actions give rise to geometric theories that go beyond the metric paradigm (even metric-less theories are possible), and contain Einstein gravity as a special case. Examples contain theories with generalizeations of Riemannian geometry. The 0-tensor case is related to dilaton gravity. These theories can give rise to new types of spontaneous Lorentz breaking and might be relevant for ``dark'' sector cosmology.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Positive tension 3-branes in an AdS(5) bulk

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conformal supergravity in twistor-string theory

Conformal supergravity arises in presently known formulations of twistor-string theory either via closed strings or via gauge-singlet open strings. We explore this sector of twistor-string theory, relating the relevant string modes to the particles and fields of conformal supergravity. We use the twistor-string theory to compute some tree level scattering amplitudes with supergravitons. Since the supergravitons interact with the same coupling constant as the Yang-Mills fields, conformal supergravity states will contribute to loop amplitudes of Yang-Mills gluons in these theories. Those loop amplitudes will therefore not coincide with the loop amplitudes of pure super Yang-Mills theory. © SISSA/ISAS 2004.

Conformal inflation from the Higgs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f ( R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

CLASSICAL EQUIVALENCE OF LAMBDA-R-PHI-2 THEORIES

It is shown that the action functional S[g, phi] = integral d4 x square-root -g[R/k(1 + klambdaphi2) + partial derivative(mu)phi partial derivative(mu)phi] describes, in general, one and the same classical theory whatever may be the value of the coupling constant lambda.

Offshore stereo measurements of gravity waves: classical epipolar and novel variational techniques

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. Classical epipolar techniques and modern variational methods are reviewed to reconstruct the sea surface from the stereo pairs sequentially in time. Current improvements of the variational methods are presented.

Theories of moral education and implementation in Indonesia: Re-energizing cultural identity and addressing future challenges

School is regarded as a site of moral training for the younger generation to encounter nation’s future challenges as well as to re-energize nation’s cultural identity. The more competitive global society led by free market trade in terms of ASEAN Economic Community (AEC), requires the school to adapt and change its curriculum more frequently. Like many other countries, Indonesian Ministry of Education and Culture has introduced and nurtured universal values and traditional values respectively through school curriculum reforms to develop students’ ability to participating in global society. This paper will describe classical and contemporary theories related to moral education that have been implemented in Indonesia’s school curriculum and school activities. The theories developed by Durkheim, Alastair MacIntyre, and Basil Bernstein will be discussed. This includes explaining how far the theories have been adopted in Indonesia and how the approaches are currently being used in Indonesian schooling. This paper suggests despite the implementation of those theories in Indonesian schools, the government needs to optimise the operation of those theories to gain significant outcomes.

Rheometry of dense granular materials: the crucial effects of gravity and confining walls

We describe here the rheological response of dense, slowly deforming granular materials to shear in a cylindrical Couette cell. All components of the stress on the outer cylinder are measured pointwise as a function of the depth, for different methods of construction of the bed that presumably lead to distinct fabrics. The static stress profiles for the different construction protocols are different, but a stress profile that is independent of construction history emerges when the granular column is sheared for sufficient time, in accord with the predictions of plasticity theories. However the qualitative features of the the stress profile under shear differs radically from the predictions of plasticity theories and data reported in earlier studies. We discuss a hypothesis for the anomalous stress profiles that was proposed recently by us, and the ways in which further experiments may to conducted to verify it.

Dance and the colonial body : re-choreographing postcolonial theories of the body

Cette dissertation traite la danse comme une catégorie d’analyse permettant de réorienter ou de ré-chorégraphier les théories postcoloniales du corps. Mon étude montre qu’ Edward Said, par exemple, décrit la danse seulement à travers le regard impérial, et que Homi Bhabha et Gayatri Spivak négligent complètement le rôle de la dance dans la construction de la subjectivité postcoloniale. Mon étude explique que Stavros Karayanni récemment explore la danse masculine et féminine comme espaces de résistance contre la domination coloniale. Toutefois, l’analyse de Karayanni met l’accent seulement sur le caractère insaisissable de la danse qui produit une ambigüité et une ambivalence dans le regard du sujet impériale. Contrairement aux approches de Said et de Karayanni, ma dissertation explore la danse comme un espace ou le corps du sujet colonisé chorégraphie son histoire collective que l’amnésie coloniale ne cesse de défigurer au moyen de l’acculturation et de marchandisation. Je soutiens que la danse nous offre la possibilité de concevoir le corps colonisé non seulement dans son ambiguïté, comme le souligne Karayanni, mais aussi dans son potentiel de raconter corporellement sa mémoire collective de l’intérieur de la domination impériale. Ma dissertation soutient que les catégories de l’ambiguïté et de l’insaisissabilité mystifient et fétichisent le corps dansant en le décrivant comme un élément évasif et évanescent. Ma dissertation inclut plusieurs traditions culturelles de manière à réorienter la recherche ethnographique qui décrit la dance comme articulation codée par une culture postcoloniale spécifique. Mon étude montre comment le corps colonisé produit un savoir culturel à partir de sa différence. Cette forme de savoir corporelle présente le corps colonisé en tant que sujet et non seulement objet du désir colonial. Méthodologiquement, cette dissertation rassemble des théories occidentales et autochtones de la danse. Mon étude considère aussi les théories postcoloniales du corps dansant à partir des perspectives hétérosexuelles et homosexuelles. En outre, mon étude examine les manières dont les quelles les théories contemporaines de la danse, postulées par Susan Foster et André Lepecki par exemple, peuvent être pertinentes dans le contexte postcolonial. Mon étude explore également le potentiel politique de l’érotique dans la danse à travers des représentations textuelles et cinématographiques du corps. L’introduction de ma dissertation a trois objectifs. Premièrement, elle offre un aperçu sur les théories postcoloniales du corps. Deuxièmement, elle explique les manières dans lesquelles on peut appliquer des philosophies contemporaines de la danse dans le contexte postcoloniale. Troisièmement, l’introduction analyse le rôle de la dance dans les œuvres des écrivains postcoloniales célèbres tels que Frantz Fanon, Wole Soyinka, Arundhati Roy, et Wilson Harris. Le Chapitre un remet en question les théories de l’ambiguïté et de l’insaisissabilité de la danse à partir de la théorie de l’érotique postulé par Audre Lorde. Ce chapitre examine le concept de l’érotique dans le film Dunia de Jocelyne Saab. Le Chapitre deux ouvre un dialogue entre les théories occidentales et autochtones de la danse à partir d’une étude d’un roman de Tomson Highway. Le Chapitre trois examine comment l’écrivain Trinidadien Earl Lovelace utilise la danse de carnaval comme espace culturel qui reflète l’homogénéité raciale et l’idéologie nationaliste à Trinidad et en les remettant également en question.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.