Made available in DSpace on 2014-06-11T19:31:24Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-12-20Bitstream added on 2014-06-13T20:41:38Z : No. of bitstreams: 1 sanoja_a_dr_ift.pdf: 582908 bytes, checksum: 608a543719b2da86f0b937d5c00bfbba (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fazemos uma revisão do modelo cosmológico padrão, apresentando suas bases observacionais e mostrando os aspectos conceituais mais relevantes. Depois realizamos uma revisão da teoria de in ação, indicando as motivações conceituais que levaram à formulação da teoria, o mecanismo que faz possível a in ação cósmica e como esse processo resolve os problemas clássicos da cosmologia padrão. Após mostrar que a in ação é um mecanismo bem-sucedido para explicar a origem das perturbações de densidade primordiais, concentramo-nos em descrever a evolução das perturbações de densidade cosmológica, tanto na sua fase linear como não-linear. Além disso, mostramos como o campo de perturbações de densidade linear permite predizer estatisticamente a abundância e a distribuição das estruturas cósmicas. Posteriormente, consideramos a expansão acelerada do universo e discutimos os candidatos que têm sido propostos para tentar explicar a origem dessa aceleração, especialmente o candidato da energia escura, no qual nos detemos para revisar os modelos básicos propostos com respeito à sua natureza. Adicionalmente, mostramos como sua presença afeta a evolução das perturbações de densidade. Finalmente, baseandonos no modelo de Lemaître-Tolman-Bondi, fazemos uma generalização do modelo do colapso esférico para estudar a evolução não-linear de perturbações de densidade inhomogêneas, tanto em um universo Einstein-de Sitter como em um universo CDM / We present a review of the standard cosmological model, showing both its observational basis as well as the most revelant conceptual aspects. Subsequently, we give an overview of the in ation theory , pointing out the conceptual motivations that led to its formulation, the mechanism that allow the cosmic in ation and how that process resolves the classical problems of the standard cosmology. After showing that the in ation theory provides a successful mechanism to explain the origin of the primordial density perturbations, we focus on describing the evolution of the cosmological density perturbations, both in linear and nonlinear phase. On the other hand, we show how the linear density perturbation eld allows to predict statistically the abundance and distribution of the cosmic structures. Next, we consider the accelerated expansion of the universe and mention the candidates that have seen proposed to try to explain the origin of the acceleration; especially the dark energy candidate, in which we pause to examine the basic models proposed about its nature. Further, we expose how its presence a ects the evolution of the density perturbations. Finally, based on the Lemaître-Tolman-Bondi, we make a generalization of the spherical collapse model to study the evolution of inhomogeneous nonlinear density perturbations, both in an Einstein-de Sitter as CDM universe

Orientador: Rogério Rosenfeld / Banca: José Geraldo Pereira / Banca: Hélio Vasconcelos Fagundes / Banca: Elcio Abdalla / Banca: Alberto Vazquez Saa / Resumo: Fazemos uma revisão do modelo cosmológico padrão, apresentando suas bases observacionais e mostrando os aspectos conceituais mais relevantes. Depois realizamos uma revisão da teoria de in ação, indicando as motivações conceituais que levaram à formulação da teoria, o mecanismo que faz possível a in ação cósmica e como esse processo resolve os problemas clássicos da cosmologia padrão. Após mostrar que a in ação é um mecanismo bem-sucedido para explicar a origem das perturbações de densidade primordiais, concentramo-nos em descrever a evolução das perturbações de densidade cosmológica, tanto na sua fase linear como não-linear. Além disso, mostramos como o campo de perturbações de densidade linear permite predizer estatisticamente a abundância e a distribuição das estruturas cósmicas. Posteriormente, consideramos a expansão acelerada do universo e discutimos os candidatos que têm sido propostos para tentar explicar a origem dessa aceleração, especialmente o candidato da energia escura, no qual nos detemos para revisar os modelos básicos propostos com respeito à sua natureza. Adicionalmente, mostramos como sua presença afeta a evolução das perturbações de densidade. Finalmente, baseandonos no modelo de Lemaître-Tolman-Bondi, fazemos uma generalização do modelo do colapso esférico para estudar a evolução não-linear de perturbações de densidade inhomogêneas, tanto em um universo Einstein-de Sitter como em um universo CDM / Abstract: We present a review of the standard cosmological model, showing both its observational basis as well as the most revelant conceptual aspects. Subsequently, we give an overview of the in ation theory , pointing out the conceptual motivations that led to its formulation, the mechanism that allow the cosmic in ation and how that process resolves the classical problems of the standard cosmology. After showing that the in ation theory provides a successful mechanism to explain the origin of the primordial density perturbations, we focus on describing the evolution of the cosmological density perturbations, both in linear and nonlinear phase. On the other hand, we show how the linear density perturbation eld allows to predict statistically the abundance and distribution of the cosmic structures. Next, we consider the accelerated expansion of the universe and mention the candidates that have seen proposed to try to explain the origin of the acceleration; especially the dark energy candidate, in which we pause to examine the basic models proposed about its nature. Further, we expose how its presence a ects the evolution of the density perturbations. Finally, based on the Lemaître-Tolman-Bondi, we make a generalization of the spherical collapse model to study the evolution of inhomogeneous nonlinear density perturbations, both in an Einstein-de Sitter as CDM universe / Doutor

<p>This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. </p><p>The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. </p><p>The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between <i>n</i> cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. </p><p>Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only. </p>

This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between n cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only.