In this work, we studied three selected problems in FRW spacetime. In the first part, we analysed the motion of a test particle in the homogeneous and isotropic universe. We presented a framework in which one can derive the uniformly accelerated trajectory and geodesic motion if a scale factor for a given spacetime is provided as a function of coordinate time. By applying the confomal time transformation, we were able to convert second order differential equations of motion in FRW spacetime to first order differential equations. From this, we managed to obtain a formalism to derive the uniformly accelerated trajectory of a test particle in spatially curved FRW spacetime. The second part of this work is devoted to dynamical cosmology. In particular, we analyse the cases of barotropic fluids and non-minimally coupled scalar field in spatially curved FRW spacetime. First, we set up the dynamical systems for an unspecified EoS of a barotropic fluid case and an unspecified positive potential for a non-minimal coupled scalar field case. For both of these systems, we determined well-defined dynamical variables valid for all curvatures. In the framework of these general setups we discovered several characteristic features of the systems, such as invariant subsets, symmetries, critical points and their...

O conceito de inflação foi introduzido inicialmente para resolver alguns problemas que a cosmologia de Big Bang original não conseguia explicar, tais como os problemas do horizonte e da planura. Na fase inflacionária, o universo sofre uma expansão acelerada ( ¨a > 0) em um curto período de tempo, durante o qual também são produzidas as perturbações de densidade que são responsáveis pela formação das estruturas de larga escala no universo. Os modelos cosmológicos mais simples descritos na literatura são governados por um campo escalar , chamado inflaton, minimamente acoplado à gravidade de Einstein, e sujeito a um potencial de auto-interação V (). O ingrediente crucial da inflação é a sua evolução temporal lenta (slow roll), na qual o potencial V () supera o termo de energia cinética 2/2 ao produzir esta expansão acelerada. Nesta tese, considera-se uma Lagrangiana generalizada para o inflaton dada por f(R, ,X) a fim de se estudar modelos cosmológicos, principalmente em suas fases inflacionárias. Esta Lagrangiana engloba todos os tipos de teoria da gravidade descritos na literatura, tais como os modelos de gravidade de acoplamento mínimo (quintessência, energia de phantom, k-inflação ou k-essência) e os modelos de gravidade escalar tensorial tais como os modelos de Brans-Dicke, de acoplamento não-mínimo e de gravidade modificada. Nosso principal interesse está em descrever os tipos de singularidades de modelos cosmológicos anisotrópicos e homogêneos, com ênfase especial no caso f(R, ,X) = f(R, ) + p(,X), onde f(R, ) representa um termo de acoplamento não-mínimo e p(,X) o termo não-canônico de energia cinética. O estudo de tais singularidades põe diversos vínculos para a viabilidade de modelos cosmológicos envolvendo Lagrangianas de gravidade generalizada. / The concept of inflation was firstly introduced in order to solve some problems that the original Big Bang cosmology could not explain such as the flatness and the horizon problems. In the inflationary phase, the Universe undergoes an accelerating expansion (¨a > 0) for a short time during which there is the production of the density perturbations that are responsible for the formation of the large scale structures in the Universe. The simplest cosmological models found in the literature are governed by a scalar field , called inflaton, minimally coupled to the Einstein gravity and subjected to a self-interaction potential V (). The crucial ingredient of the inflation is its slow time evolution (slow roll) in which the self-interaction potential V () overcomes the kinetic energy term 2/2 and produces this accelerating expansion. In this thesis, we consider a generalized Lagrangian given by f(R, ,X) to study cosmological models, mainly in their inflationary phases. This Lagrangian comprehends any type of gravity theory found in the literature such as the minimal coupling gravity (i.e. quintessence, phantom energy, k-inflation or k-essence models) and the scalar-tensor gravity such as Brans-Dicke, non-minimal coupling and modified gravity models. We are specially interested in describing the types of singularities that can be found in anisotropic and homogeneous cosmological models in which the Lagrangian assumes the particular form f(R, ,X) = f(R, ) + p(,X), where f(R, ) represents the non-minimal coupling term and p(,X) is the non-canonical kinetic term. The study of these singularities stablishes many constraints for the viability of cosmological models presenting a generalized gravity Lagrangian.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T12:14:57Z No. of bitstreams: 1 arquivototal.pdf: 2895129 bytes, checksum: 572a06d99b50bb3cd9314e80d1c5b3c7 (MD5) / Made available in DSpace on 2017-09-18T12:14:57Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2895129 bytes, checksum: 572a06d99b50bb3cd9314e80d1c5b3c7 (MD5) Previous issue date: 2017-07-27 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this dissertation, we study the possibility of violation of the Lorentz invariance taking into account some terms of the standard extended model, more specifically, the part of this model that deals with the extended quantum electrodynamics. We perform quantum corrections in the fermionic sector of the usual quantum electrodynamics added with terms that violate the Lorentz symmetries and in two different configurations. First, the coefficient added and that causes the Lorentz symmetry breaking is introduced th­rough the constant pseudo-tensor Ic juvAp And we treat the constant electric and magnetic fields, that is, we do not evaluate as external leg between the coupling of the photon and fermions, evaluating the field FAp Without opening in term of the gauge field. In the second case, we investigated the operators governed by the coefficient of interaction FAp open in term of the gauge field. In the second case, we investigated the mixed contribu­tion of the minimum and non-minimum coupling. We immediately know that for each coupling evaluated will have their respective vertices. For both cases, we calculate the quantum corrections in a loop. In the first case, the theory with the coefficient Ic juvAp and field FAp without being opened at the end of the gauge field AP, The contribution of a loop and we calculate the counter-ter, having a CPT-par characteristic, which will be useful to be introduced in action to eliminate divergences. In the second case, we examined the contribution of a loop, considering the mixture of minimum and non-minimum coupling, that is, and and and an external one AP, having a CPT-par characteristic, One related to the non-minimum coupling and another to the minimum, respectively and verifying the vertex correction also having the contribution of its counter-term. / Nesta dissertagao, estudamos a possibilidade de violagao da invariancia de Lorentz le­vando em conta alguns termos do modelo padrao estendido, mais especificamente da parte do modelo que trata da eletrodinamica quantica estendida. Realizamos corregoes quanticas no setor fermiOnico da eletrodinamica quantica usual adicionada de termos que violam as simetrias de Lorentz e em duas configuragoes diferentes. Primeiramente, o co­eficiente adicionado e que ocasiona a quebra de simetria de Lorentz é introduzida atraves do pseudo-tensor constante is juvAp e tratamos os campos eletricos e magneticos constantes, ou seja, nao avaliamos como perna externas entre o acoplamento do fOton e fermions, avaliando o campo FAp sem abrir em termo do campo de gauge. No segundo caso, investi­gamos a contribuigao mista do acoplamento minim° e nao-minimo. De imediato sabemos que para cada acoplamento avaliado tera seus respectivo vertices. Para os dois casos, cal­culamos as corregoes quanticas em um lago. No primeiro caso, a teoria com o coeficiente I c juvAp e campo FAp sem ser aberto em termo do campo de gauge AP, a contribuigao de um lago e calculamos a pega de polo, tendo uma caracteristica CPT-par, que sera iltil para ser introduzida na agao para eliminar as divergencias. No segundo caso, nos examinamos a contribuigao de um lago, considerando a mistura dos acoplamento minimo e nao-minimo, ou seja, um Fill, e um externo AP, tendo como caracteristica CPT-impar um relacionado ao acoplamento nao-minimo e outro ao minimo, respectivamente e verificando a corregao de vertice tendo tambem a contribuigao do seu contra termo.

O conceito de inflação foi introduzido inicialmente para resolver alguns problemas que a cosmologia de Big Bang original não conseguia explicar, tais como os problemas do horizonte e da planura. Na fase inflacionária, o universo sofre uma expansão acelerada ( ¨a > 0) em um curto período de tempo, durante o qual também são produzidas as perturbações de densidade que são responsáveis pela formação das estruturas de larga escala no universo. Os modelos cosmológicos mais simples descritos na literatura são governados por um campo escalar , chamado inflaton, minimamente acoplado à gravidade de Einstein, e sujeito a um potencial de auto-interação V (). O ingrediente crucial da inflação é a sua evolução temporal lenta (slow roll), na qual o potencial V () supera o termo de energia cinética 2/2 ao produzir esta expansão acelerada. Nesta tese, considera-se uma Lagrangiana generalizada para o inflaton dada por f(R, ,X) a fim de se estudar modelos cosmológicos, principalmente em suas fases inflacionárias. Esta Lagrangiana engloba todos os tipos de teoria da gravidade descritos na literatura, tais como os modelos de gravidade de acoplamento mínimo (quintessência, energia de phantom, k-inflação ou k-essência) e os modelos de gravidade escalar tensorial tais como os modelos de Brans-Dicke, de acoplamento não-mínimo e de gravidade modificada. Nosso principal interesse está em descrever os tipos de singularidades de modelos cosmológicos anisotrópicos e homogêneos, com ênfase especial no caso f(R, ,X) = f(R, ) + p(,X), onde f(R, ) representa um termo de acoplamento não-mínimo e p(,X) o termo não-canônico de energia cinética. O estudo de tais singularidades põe diversos vínculos para a viabilidade de modelos cosmológicos envolvendo Lagrangianas de gravidade generalizada. / The concept of inflation was firstly introduced in order to solve some problems that the original Big Bang cosmology could not explain such as the flatness and the horizon problems. In the inflationary phase, the Universe undergoes an accelerating expansion (¨a > 0) for a short time during which there is the production of the density perturbations that are responsible for the formation of the large scale structures in the Universe. The simplest cosmological models found in the literature are governed by a scalar field , called inflaton, minimally coupled to the Einstein gravity and subjected to a self-interaction potential V (). The crucial ingredient of the inflation is its slow time evolution (slow roll) in which the self-interaction potential V () overcomes the kinetic energy term 2/2 and produces this accelerating expansion. In this thesis, we consider a generalized Lagrangian given by f(R, ,X) to study cosmological models, mainly in their inflationary phases. This Lagrangian comprehends any type of gravity theory found in the literature such as the minimal coupling gravity (i.e. quintessence, phantom energy, k-inflation or k-essence models) and the scalar-tensor gravity such as Brans-Dicke, non-minimal coupling and modified gravity models. We are specially interested in describing the types of singularities that can be found in anisotropic and homogeneous cosmological models in which the Lagrangian assumes the particular form f(R, ,X) = f(R, ) + p(,X), where f(R, ) represents the non-minimal coupling term and p(,X) is the non-canonical kinetic term. The study of these singularities stablishes many constraints for the viability of cosmological models presenting a generalized gravity Lagrangian.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18069号 / 理博第3947号 / 新制||理||1569(附属図書館) / 30927 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 田中 貴浩, 教授 畑 浩之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Pendant les deux dernières décennies l'idée d'une nature holographique de la gravité a pris forme à travers la correspondance AdS/CFT, aussi connue sous le nom de dualité jauge/gravité. CFT correspond à « conformal field theory », théorie conforme des champs, et dans la dualité il s'agit d'une théorie de jauge dans la limite de grand N 1. AdS représente l'espace d'anti-de Sitter, une solution maximalement symétrique des équations d'Einstein avec une constante cosmologique négative, et correspond au côté gravitationnel de la dualité. Dans certaines limites, des théories sur AdS avec de la gravité en d+1 dimensions peuvent être associées à des CFTs sans gravité en d dimensions, d'où le nom « dualité ». Cette dualité est aussi dite « holographique » par analogie avec le concept optique homonyme qui indique la possibilité de générer une image tridimensionnelle comme la projection d'un écran ou d'un film bidimensionnel. Le terme holographie vient des mots grecs holos, « en entier », et graphe, « écriture. Une telle projection, malgré le fait que l'information est stockée en 2 dimensions, contiendrait toute l'information pour reconstruire l'image tridimensionnelle. Dans la dualité jauge/gravité, la théorie de jauge se comporte comme un film d-dimensionnel qui contient la même information que l'image gravitationnelle (d+1)-dimensionnelle. Cette dualité relie la théorie gravitationnelle à la théorie quantique de champs (TQC) dual à travers des conditions aux limites sur des champs qui vivent dans AdS. Dans ce sens-là, la théorie de jauge peut être considérée comme définie sur le bord d'AdS, ce qui renforce l'analogie optique et, pour cela, la dualité est aussi connue comme la correspondance « bulk/boundary » ou « intérieur/bord ». Une de ses principales propriétés est l'association d'une TQC fortement couplée à une théorie gravitationnelle faiblement couplée et vice-versa. Pour cette raison, dans cette thèse j'utilise un intérieur faiblement couplé pour explorer et identifier des propriétés non-perturbatives de TQCs dans la limite de couplage fort. Cette thèse explore l'holographie à température nulle et finie. Nos objets d'intérêt sont des TQCs générées par la brisure de l'invariance d'échelle de CFTs et qui peuvent être étudiées à travers le groupe de renormalisation (GR). Le profil des champs au long de la dimension supplémentaire à l'intérieur est dual à des flots du GR sur la TQC vivant sur le bord, car la dimension supplémentaire est en correspondance avec l'échelle d'énergie. La correspondance va plus loin en identifiant les champs de l'intérieur comme duaux aux couplages renormalisés de la TQC, ce qui mène au concept du GR holographique. Avec le GR holographique, dans cette thèse je vais explorer des comportements qui sont d'une nature intrinsèquement non-perturbatifs du point de vue de la QFT. Les principaux résultats sont les suivants. A température nulle, pour un seul couplage, nous avons classifié toutes les solutions de notre système et identifié trois types de flots exotiques correspondant à des solutions qui inversent leur direction au long du flot, d'autres qui sautent des points fixes et des flots qui interpolent entre des minima du potentiel. Ces résultats ont été généralisés à plusieurs couplages à température nulle. Je présente également la relation entre la fonction principale de Hamilton et la nature du champ de vitesses des couplages: gradient ou non. À température finie nous avons considéré un seul couplage et exploré la thermodynamique des trois types de solutions exotiques mentionnées ci-dessus. Nous avons identifié une transition de phase entre des solutions qui sautent et qui ne sautent pas des points fixes, une discontinuité de l'énergie libre pour un potentiel admettant des solutions qui inversent le sens du flot à température nulle et la non-existence de solutions à température finie associées à un flot entre minima pour un potentiel qui admet une telle solution à température nulle. / Over the past twenty years the idea that gravity is holographic has become progressively concrete, materialised through the AdS/CFT correspondence, also known as the gauge/gravity duality. CFT stands for conformal field theory and in the correspondence it is a gauge-theory in the large N limit1. AdS stands for anti-de Sitter space-time, a maximally symmetric solution of Einstein’s equations with negative cosmological constant, it corresponds to the gravitational side of the duality. In some limits, theories on AdS with gravity in d + 1 dimensions can be mapped to CFTs without gravity in d dimensions and vice-versa, hence the name “duality”. Another term for the gauge/gravity duality is holographic duality. The term holography comes from the Greek words holos, “whole”, and graphe, “writing” or “drawing”. In physics, the term holography originates in optics, referring to the possibility of generating a 3-dimensional image as a projection from a bi- dimensional screen or film. In such a projection, despite of the fact that the film has one spatial dimension less than the projection, the film would contain all the information to recover the three-dimensional image. In the gauge/gravity duality, the gauge-theory behaves as a d-dimensional film which contains the same information as the (d + 1)-dimensional gravitational image. This analogy is reinforced by the fact that the duality relates the gravitational theory to the dual resulting quantum field theory (QFT) via boundary conditions of the fields living in the AdS bulk. In this sense, the gauge theory can be thought of as living at the boundary of AdS and the duality is also know as the bulk/boundary correspondence. One of the most important features of the correspondence is the mapping of a strongly coupled QFT into a weakly coupled gravitational theory and vice-versa. For this reason, in this thesis I will use a weakly coupled bulk theory to explore and identify non-perturbative features of QFT in the strong coupling regime. This thesis explores holography at zero and finite temperature. Our main concern are the CFTs in which scale invariance is either spontaneously or explicitly broken and the resulting QFT can be studied via the renormalisation group (RG). The profile of fields along the extra-dimension in the bulk is dual to renormalisation group flows in the QFT side (boundary), as the extra-dimension can be mapped to an energy scale. The mapping goes further by identifying bulk fields as dual to QFT running couplings, leading to the so-called holographic renormalisation group. With the holographic RG in what follows I will explore behaviours that are of an intrinsically non-perturbative nature from the QFT standpoint. The main results are as follows. At zero temperature, for a single coupling, we classified all possible solutions in our setup and identified three kinds of exotic flows corresponding to solutions reversing direction along the flow (bounces), flows skipping fixed points and solutions interpolating between minima of the potential. These results are generalised to many couplings at zero temperature. I also present a complete map between forms of the Hamilton's principal function and the gradient or non-gradient nature of the solutions. At finite temperature we considered a single coupling setup and explored the thermodynamics of the three kinds of above-mentioned exotic flows. We identified a phase transition between skipping and non-skipping solutions, a discontinuous free energy for a bouncing potential and the non-existence of a finite-temperature solutions for a chosen potential admitting a minimum-to-minimum solution.

Made available in DSpace on 2015-05-14T12:14:00Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1354058 bytes, checksum: 2f549ef4aed5937520237cd0b6df944f (MD5) Previous issue date: 2011-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Since many models in physics depend on the confinement of particles in certain regions of the space-time, like Rubakov and Randall-Sundrum models, we analyze the possibility of using geometrical fields to confine particles. In doing so, we exhibit some examples of the confinement of particles by using only geometrical fields such as torsion and Weyl 1- form. In order to prepare the reader to these examples, we give a brief introduction to the Riemannian and the non-Riemannian geometries. It turned out to be impossible to avoid controversial issues such as the equation of motion of a particle, the use of the minimal coupling procedure, and the application of the variational principle for non-Riemannian geometries. However, we avoided choosing what approach was right and decided to take two completely different approaches into account, namely, Kleinert's and Hehl's ones. Kleinert claims that particles must follow autoparallel, while Hehl and others state that the equation of motion of a particle must be derived from a conservation law related to the energy-momentum tensor of the particle. As a matter of fact, there are more differences between those approaches than we have mentioned here, but we expect this thesis to clarify those differences. To be more precise, we managed to exhibit examples of confinement only for Kleinert's approach. We had dificulty finding a example of confinement to hehl's approach, however we were able to eliminate the possibility of confinement for many cases, like scale fields for example. / Levando em consideração o interesse visível que muitos modelos da física têm em manter a matéria usual confinada em uma certa região do espaço-tempo, como por exemplo o modelo de Rubakov e o de Randall-Sundrum, exibimos a possibilidade da utilização de campos com origem geométrica para realizar este confinamento. Antes, porém, preparamos o leitor com todo o aparato geométrico necessário para a compreensão do que é feito nos últimos capítulos desta tese. Tornou-se impossível fugir de questões polêmicas envolvendo geometrias mais gerais que a riemanniana, como por exemplo a polêmica sobre a equação de movimento da partícula, o uso do acoplamento mínimo e a aplicação do princípio variacional. Entretanto, tentamos adotar uma postura imparcial e fizemos a análise do confinamento seguindo duas vertentes distintas. Uma das vertentes, defendidas por Kleinert, consiste em postular que partículas seguem autoparalelas. A outra vertente, a mais comum na literatura, segue a linha de Hehl, Gasperini e outros. Nesta vertente, a equação de movimento de uma partícula não pode ser postulada, mas sim obtida a partir da lei de conservação associada ao tensor de energia-momento da partícula, pois este contém informação sobre o movimento da partícula. Há mais diferenças entre essas duas linhas do que citamos aqui, como será indicado no decorrer da tese. Para ser mais preciso, fomos capazes de exibir o confinamento apenas para a primeira vertente. No caso da segunda, dificuldades técnicas nos limitaram a somente descartar certos campos de origem geométrica como campos confinadores.