Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

Neste trabalho, construímos novas soluções com simetria esférica ou axial para as equações do campo gravitacional induzido num cenário brana do tipo Randall-Sundrum, onde uma 3-brana com constante cosmológica está imersa num espaço-tempo 5-dimensional conhecido como bulk. Para o caso esfericamente simétrico, com constante cosmológica negativa, obtivemos uma família de soluções numa brana assintoticamente anti-de Sitter, sendo que cada membro desta é diferenciado de outro por uma constante integração C, que fixada proveu-nos soluções de buracos negros ou buracos de minhocas. Com a mesma simetria, geometrias que descrevem buracos de minhoca foram encontradas numa brana assintoticamente de Sitter. Para o caso axialmente simétrico, métricas assintoticamente anti-de Sitter e de Sitter foram construídas no contexto citado. Propriedades óticas, como a rotação do vetor de polarização, foram estudadas, mostrando-nos algumas diferenças entre os mundos brana, tratados como uma teoria de gravitação modificada, e a relatividade geral. / In this work we have constructed new solutions, with axial or spherical symmetry, to the induced gravitational field equations within a Randall-Sundrum type brane world scenario, where a 3-brane with cosmological constant is embedded in a 5-dimensional space-time called bulk. For the spherical case with negative cosmological constant, we have found a family of solutions in an anti-de Sitter brane, where each member of the family is different from another when C is fixed. With a fixed C we have black holes or wormholes. In this same case, with spherical symmetry, we have obtained wormhole solutions in a de Sitter brane. In the same context, for the axially symmetric case, metrics asymptotically anti-de Sitter and de Sitter were built. Optics features, like rotation of polarization vector, have been studied. These features showed some differences between brane worlds, a theory of modified gravity, and the General Relativity.

Cette thèse est consacrée à l'analyse, dans le cadre des théories supersymétriques, des phénomènes liés à la présence de dimensions supplémentaires et de secteurs branaires. Nous proposons une extension du MSSM motivé par les théories présentant des dimensions supplémentaires, dans laquelle le secteur de jauge est étendu de manière à former une représentation N = 2 de l'algèbre de supersymétrie. Nous décrivons comment, dans ce modèle, des masses de Dirac apparaissent naturellement pour les jauginos, et calculons les interactions et matrices de masse des nouveaux neutralinos et charginos présents. Puis nous étudions, dans le cadre des théories de supergravité en cinq dimensions, le couplage des champs de gravité aux multiplets chiraux localisés sur les branes. Cette étude conduit à l'introduction d'une nouvelle extension hors couche de masse de la supergravité en cinq dimensions, qui est bien adaptée au couplage des champs chiraux sur les branes au multiplet de supergravité pentadimensionnelle dans le cas d'un superpotentiel quelconque et dans la présence de F-termes différents de zéro. Le mécanisme de Scherk-Schwarz généralisé et le mécanisme de super-Higgs dans cette classe de théories sont également étudiés en détail. Notamment nous décrivons comment les pseudo-Goldstinos apparaissent lorsque la supersymétrie est brisée par des F-termes sur les branes et dans le volume pentadimensionnel par le mécanisme de Scherk-Schwarz. Nous étudions des possibilités d'identification des pseudo-Goldstinos aux neutrinos stériles. Enfin, des propriétés des gravitinos dans les théories à six dimensions sont étudiées.

Ce mémoire présente l'étude de configurations dépendantes du temps dans le formalisme de première quantification de la corde. Ces configurations sont exactes, c'est-à-dire qu'il est possible de trouver des solutions explicites de la théorie conforme à deux dimensions correspondante. Nous pouvons alors calculer perturbativement les amplitudes de corde et nous en servir pour comprendre l'interaction entre la géométrie dépendante du temps et la corde quantifiée. Après une présentation dans le premier chapitre de la démarche qui a mené à cette étude, le formalisme perturbatif de première quantification est exposé de manière détaillée dans un second chapitre et une partie des difficultés techniques sont résolues. Dans un troisième chapitre, nous expliquons les phénomènes physiques correspondant aux différentes configurations et nous exposons les résultats que nous avons obtenus. Enfin, un bref chapitre conclut et ouvre les perspectives de ce travail de thèse.

During inflation quantum fluctuations of the field driving inflation, known as inflaton, were stretched by inflationary expansion to galactic size scales or even larger. A possible implication of inflation -- if it is correct -- is that our observable universe was once of sub-Planckian size. Thus inflation could act as a magnifier to probe the short distance structure of space-time. General arguments about the quantum theory of gravity suggest that the short distance structure of space-time can be modeled as arising from some corrections to the well-known uncertainty relation between the position and momentum operators. Such modifications have been predicted by more fundamental theories such as string theory. This modified commutation relation has been implemented at the first quantized level to the theory of cosmological perturbations. In this thesis, we will show that the aforementioned scenario of implementing the minimal length to the action has an ambiguity: total time derivatives that in continuous space-time could be neglected and do not contribute to the equations of motion, cease to remain total time derivatives as we implement minimal length. Such an ambiguity opens up the possibility for trans-Planckian physics to leave an imprint on the ratio of tensor to scalar fluctuations. In near de-Sitter space, we obtain the explicit dependence of the tensor/scalar on the minimal length. Also the first consistency relation is examined in a power-law background, where it is found that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably as it leads to large oscillations in the scalar spectral index in the observable range of scales. In the second part of the thesis, I demonstrate how the assumption of existence of invariant minimal length can assist us to explain the origin of cosmic magnetic fields. The third part of the thesis is dedicated to the study of signatures of M-theory Cascade inflation.

During inflation quantum fluctuations of the field driving inflation, known as inflaton, were stretched by inflationary expansion to galactic size scales or even larger. A possible implication of inflation -- if it is correct -- is that our observable universe was once of sub-Planckian size. Thus inflation could act as a magnifier to probe the short distance structure of space-time. General arguments about the quantum theory of gravity suggest that the short distance structure of space-time can be modeled as arising from some corrections to the well-known uncertainty relation between the position and momentum operators. Such modifications have been predicted by more fundamental theories such as string theory. This modified commutation relation has been implemented at the first quantized level to the theory of cosmological perturbations. In this thesis, we will show that the aforementioned scenario of implementing the minimal length to the action has an ambiguity: total time derivatives that in continuous space-time could be neglected and do not contribute to the equations of motion, cease to remain total time derivatives as we implement minimal length. Such an ambiguity opens up the possibility for trans-Planckian physics to leave an imprint on the ratio of tensor to scalar fluctuations. In near de-Sitter space, we obtain the explicit dependence of the tensor/scalar on the minimal length. Also the first consistency relation is examined in a power-law background, where it is found that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably as it leads to large oscillations in the scalar spectral index in the observable range of scales. In the second part of the thesis, I demonstrate how the assumption of existence of invariant minimal length can assist us to explain the origin of cosmic magnetic fields. The third part of the thesis is dedicated to the study of signatures of M-theory Cascade inflation.

Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

Neste trabalho, construímos novas soluções com simetria esférica ou axial para as equações do campo gravitacional induzido num cenário brana do tipo Randall-Sundrum, onde uma 3-brana com constante cosmológica está imersa num espaço-tempo 5-dimensional conhecido como bulk. Para o caso esfericamente simétrico, com constante cosmológica negativa, obtivemos uma família de soluções numa brana assintoticamente anti-de Sitter, sendo que cada membro desta é diferenciado de outro por uma constante integração C, que fixada proveu-nos soluções de buracos negros ou buracos de minhocas. Com a mesma simetria, geometrias que descrevem buracos de minhoca foram encontradas numa brana assintoticamente de Sitter. Para o caso axialmente simétrico, métricas assintoticamente anti-de Sitter e de Sitter foram construídas no contexto citado. Propriedades óticas, como a rotação do vetor de polarização, foram estudadas, mostrando-nos algumas diferenças entre os mundos brana, tratados como uma teoria de gravitação modificada, e a relatividade geral. / In this work we have constructed new solutions, with axial or spherical symmetry, to the induced gravitational field equations within a Randall-Sundrum type brane world scenario, where a 3-brane with cosmological constant is embedded in a 5-dimensional space-time called bulk. For the spherical case with negative cosmological constant, we have found a family of solutions in an anti-de Sitter brane, where each member of the family is different from another when C is fixed. With a fixed C we have black holes or wormholes. In this same case, with spherical symmetry, we have obtained wormhole solutions in a de Sitter brane. In the same context, for the axially symmetric case, metrics asymptotically anti-de Sitter and de Sitter were built. Optics features, like rotation of polarization vector, have been studied. These features showed some differences between brane worlds, a theory of modified gravity, and the General Relativity.

This project is an investigation of a cosmological model consisting of a five dimensional AdS-vacuum with a flux. By discharges in the flux, four dimensional bubbles can nucleate in the vacuum and collide with each other while expanding. Our observable universe is considered to be localized on the membrane of such a bubble. The main purpose of the model was to find a possible explanation for dark energy and inflation. We compute the Friedmann equation for an expanding bubble, as well as analytical expressions for the two slow roll parameters ε and η related to slow roll inflation. We also show that there exists a set of parameters of the model where both slow roll parameters are small enough in order for inflation to last for at least 60 Hubble times. However, our model doesn’t survive all consistency checks with today’s observations. We conclude that even if the resulting slow roll parameters look promising, one has to either look harder for a set of ”good” fundamental parameters of the model, or further develop it to have a chance of surviving all consistency checks. / Populärvetenskaplig sammanfattning: Det här projektet undersöker en kosmologisk modell bestående av ett femdimensionellt vakuum med negativ rumtidkrökning. I vakuumet finns ett elektriskt fält, som i högre dimensioner än fyra kallas flux (flöde). Urladdningar i detta flux gör det möjligt för fyrdimensionella bubblor att uppstå i vakuumet. Dessa vakuumbubblor expanderar snabbt och kommer så småningom att kollidera med varandra. Tanken är att vårt fyrdimensionella observerbara universum utgör en del av membranet på en av dessa expanderande vakuumbubblor. De andra vakuumbubblorna kan - om man vill - betraktas som parallella universum. Målet med detta projekt har varit att hitta en möjlig model för kosmisk inflation - epoken i vårt universums ungdom då rummet expanderade enormt snabbt under en väldigt kort tidsperiod. Inflationen i vår modell äger rum när vakuumbubblan för vårt universum kolliderar med andra vakuumbubblor. Vi lyckades visa att den här modellen kan ge upphov till inflation som varar tillräckligt länge för att det ska stämma överens med dagens observationer av vårt observerbara universum. Dock förutspår modellen även andra saker som inte stämmer överens med observationerna. Vår slutsats är att modellen ser lovande ut, men att man antingen behöver undersöka den noggrannare eller utveckla den på något sätt, om den ska ha en chans att stämma överens med universumet vi observerar. / <p>Presentationen skedde över videolänk på grund av Covid-19.</p>

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24403号 / 理博第4902号 / 新制||理||1700(附属図書館) / 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 高柳 匡, 教授 杉本 茂樹, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM