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.

Dans ce manuscrit, nous présentons un mise en place et calcul d'un observable physique dans le cadre de la Gravité Quantique à Boucles covariante, pour un processus physique mettant en jeu la gravité quantique de façon non-perturbatif. Nous considerons la transition d'une région de trou noir à une région de trou blanc, traitée comme une transition de géométrie assimilable à un effet de tunnel gravitationnel. L'observable physique est le temps caractéristique dans lequel ce processus se déroule.Nous commençons par une dérivation formelle de haut--en--bas, allant de l'action de Hilbert-Einstein au ansatz qui définit les amplitudes de l'approche covariante de la GQB. Nous prenons ensuite le chemin de bas--en--haut, aboutissant à l'image d'une intégrale de chemin du type somme-de-géométries qui émerge à la limite semi-classique, et discutons son lien étroite avec une intégrale de chemin basé sur l'action de Regge. En suite, nous expliquons comment construire des paquets d'ondes décrivant des géométries spatiales quantiques, plongées dans un espace-temps quantique de signature Lorentzienne.Nous montrons que lors de la mise en œuvre de ces outils, nous avons une estimation simple des amplitudes décrivant des transitions de géométrie de façon probabiliste. Nous construisons un mise en place basée sur l'espace-temps Haggard-Rovelli, où une approche d'intégrale de chemin peut être appliquée naturellement. Nous procédons à une dérivation d'une expression explicite, analytiquement bien--définie et finie, pour une amplitude de transition décrivant ce processus. Nous utilisons ensuite l'approximation semi-classique pour estimer le temps caractéristique du phénomène. / In this manuscript we present a calculation from covariant Loop Quantum Gravity, of a physical observable in a non-perturbative quantum gravitational physical process. The process regards the transition of a trapped region to an anti--trapped region and is treated as a quantum geometry transition akin to gravitational tunneling. The physical observable is the characteristic timescale in which the process takes place. We start with a top--to--bottom formal derivation of the ansatz defining the amplitudes for covariant LQG, starting from the Hilbert-Einstein action. We then take the bottom--to--top path, starting from the EPRL ansatz, to the sum--over--geometries path integral emerging in the semi-classical limit, and discuss its close relation to the naive path integral over the Regge action. We proceed to the construction of wave--packets describing quantum spacelike three-geometries that include a notion of embedding in a Lorentzian spacetime. We derive a simple estimation for the amplitudes describing geometry transition and show that a probabilistic description for such phenomena emerges, with the probability of the phenomena to take place being in general non-vanishing.The Haggard-Rovelli spacetime, modelling the spacetime surrounding the geometry transition region for a black to white hole process, is formulated. We then use the semi--classical approximation to give a general estimation of amplitudes describing the process. We conclude that the transition is predicted to be allowed by LQG, with a crossing time that is linear in the mass. The probability for the process to take place is suppressed but non-zero.