Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-27T11:35:41Z No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T20:52:19Z (GMT) No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Made available in DSpace on 2017-08-07T20:52:19Z (GMT). No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) Previous issue date: 2011-02-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A teoria relativística da gravitação é uma ferramenta fundamental para a compreensão da cosmologia moderna. Ela descreve a dinâmica do campo gravitacional ao longo do espaço-tempo. Dentre os possíveis modelos de universo, um dos mais comuns é o descrito pela métrica de Friedmann-Lemaitre-Robertson-Walker (FLRW). Esta métrica pode ser escrita em termos do tempo conforme e descreve um universo homogêneo e isotrópico. Neste trabalho investigamos os campos de Dirac não massivos neste modelo de universo. Os resultados mostram uma compatibilidade entre as equações de Dirac e a métrica de FLRW. Os efeitos do parâmetro de Immirzi junto com os férmions podem ser descritos em termos de um fluido perfeito usual intermediário entre a poeira e radiação. / The general relativity theory is fundamental tool for understanding the modern cosmology. In this work we investigated the massless Dirac fields in the Friedamm-Lamaitre-Robertson-Walker universe. The metric is written in terms of conformal time which describes a homogeneous and isotropic universe. We show that the effects of Immirzi parameter along with the fermions can be described in terms of a usual perfect fluid intermediate between dust and radiation.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-21T13:35:56Z No. of bitstreams: 1 cleberabrahaodesouza.pdf: 301985 bytes, checksum: 0b75cdeb57a94d3300fda08720057f94 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-12-22T12:41:11Z (GMT) No. of bitstreams: 1 cleberabrahaodesouza.pdf: 301985 bytes, checksum: 0b75cdeb57a94d3300fda08720057f94 (MD5) / Made available in DSpace on 2016-12-22T12:41:11Z (GMT). No. of bitstreams: 1 cleberabrahaodesouza.pdf: 301985 bytes, checksum: 0b75cdeb57a94d3300fda08720057f94 (MD5) Previous issue date: 2016-04-11 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresentamos a teoria de Einstein-Cartan através da ação de Holst com campos de Dirac minimamente acoplados a curvatura e torção. Um termo de acoplamento quadri-fermiônico emerge naturalmente após usar a relação entre torção e matéria, conforme resultados obtidos previamente por Perez e Rovelli. O coeficiente desse acoplamento possui uma relação direta com o parâmetro de Barbero-Immirzi (BI), presente na ação de Holst. Investigamos soluções cosmológicas para o modelo de Friedman-Lemaître-Robertson-Walker (FLRW). Mostramos que para ocasonãomassivo,aequaçãodeestadodescreveumfluidoperfeitocom p=wρ ,com w=1. Para o caso massivo, é possível descrever uma fase inflacionária com w =−1 ou w = 1 para um Universo jovem. Estudamos também o acoplamento entre gravitação, férmions e torção com um fluido de spin (fluido de Weyssenhoff). Mostramos uma ação equivalente em termos da interação quadri-fermiônica, um termo apenas de interação entre o tensor de spin, mais um termo de interação entre férmions e o tensor de spin, todos eles em função do parâmetro (BI). O termo de interação entre o fluido de spin e a corrente fermiônica representa um novo ponto de partida para a descrição de soluções cosmológicas. / In this work we present the Einstein-Cartan theory by means of Holst action with Dirac fields description minimally coupled to curvature and torsion. The coupling term four-fermion emerges after using the relationship between the torsion and source of matter, previously calculated by Perez and Rovelli. The coupling constant is related to the Barbero-Immirzi (BI) parameter, which emerges from the Holst action. We investigate cosmological solutions in the standard Friedman-Lemaître-Robertson-Walker (FLRW) model. Whe show in the massless case that the equation of state describes a perfect fluid with p = wρ, with w = 1. For the massive case, is possible to describe an inflationary phase with w = 1 for early universe. We study also the coupling between fermions and gravitation with torsion in the presence of spin fluid (Weyssenhofffluid),andweshowtheequivalentactionwithfour-fermioninteraction,atermof self-interaction of the spin fluid and a interaction term between fermionic field and spin fluid. In all these cases, there is the dependence on BI parameter. The interaction term between the fermioniccurrentandthespintensorcanbeconsideredasanewstartingframeworkforstuding cosmological effects.

Le problème de la limite continue de la gravitation quantique à boucle est encore ouvert. En effet, la dynamique précise n’est pas connue et nous ne disposons pas des outils nécessaires à l’étude de cette limite le cas échéant. Dans cette thèse, nous étudions quelques méthodes de coarse-graining (étude à gros grains) qui devraient contribuer à cette entreprise. Nous nous concentrons sur deux aspects du flot: la détermination d’observables naturelles à grandes échelles d’un côté et la manière de s’abstraire du problème de la dynamique à graphe variable en la projetant sur des graphes fixes de l'autre.Pour déterminer les observables aux grandes distances, nous étudions le cas des tétraèdres hyperboliques et leur description naturelle dans un langage proche de celui de la gravitation quantique à boucle. Les holonomies de surface en particulier jouent un rôle important. Cela dégage la structure des double spin networks constitués d'un graphe et de son dual, structure qui semble aussi apparaître dans les travaux de Freidel et al. Pour résoudre le problème des graphes variables, nous considérons et définissons les loopy spin networks. Ils encodent par des boucles la courbure locale d'un vertex effectif et permettent ainsi de décrire différents graphes en les masquant via le processus de coarse-graining. De plus, leur définition donne un procédé naturel systématique de coarse-graining pour passer d'une échelle à une autre.Ensemble, ces deux principaux résultats posent le fondement d'un programme de coarse-graining pour les théories invariantes sous difféomorphismes. / The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories.