This thesis contains two main themes. The first is Einstein's theory of general relativity in higher dimensions, while the second is M-theory. The first part of the thesis concerns the use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is explained. The first application of the tensor approach that is discussed is the systematic classification of higher dimensional axisymmetric solutions. A complete classification of all algebraically special axisymmetric solutions to the vacuum Einstein equation in higher dimensions is presented. Next, the study of perturbations of higher dimensional solutions within this framework and the possibility of decoupling equations for black hole solutions of interest, as has been successfully done in four dimensions, is considered. In the case where such a decoupling of the perturbations is possible, a map for constructing solutions of the perturbation equation is presented and is applied to the Kerr/CFT correspondence. Also, the property of gravitational radiation emitted from an isolated source in higher dimensions is considered and the tensor classification scheme is used to derive the peeling property of the Weyl tensor in higher dimensions. This is shown to be different to that which occurs in four dimensions. Finally, after an in-depth exposition of the spinor classification scheme and its relation to the tensor approach, solutions belonging to the most special type in the spinor classification are classified. In addition, the classification of the black ring in this scheme is discussed. The second part of the thesis explores the use of generalised geometry as a tool for better understanding M-theory. After briefly reviewing the curious phenomenon of M-theory dualities, it is explained how generalised geometry can be used to show that these symmetries are not exclusive to compactifications of the theory, but can be made manifest without recourse to compactification. Finally, results regarding the local symmetries of M-theory in the generalised geometry framework for a particular symmetry group are presented.

Les éphémérides planétaires jouent un rôle important pour la navigation des missions spatiales actuelles et la mise en place des missions futures ainsi que la réduction et l'analyse des observations astronomiques les plus précises. Les éphémérides planétaires actuelles (DE, INPOP, EPM)L'objectif de la thèse est d'utiliser des archives de données de missions spatiales passées et présentes et de fournir des outils d'analyse pour l'amélioration de l'éphéméride de données pour l'amélioration de l’éphéméride planétaire planétaire INPOP, ainsi que pour une meilleure utilisation des éphémérides pour effectuer des teste de la physique tels que la relativité générale, les études de la couronne solaire [...] / The planetary ephemerides play a crucial role for spacecraft navigation, mission planning, reductionand analysis of the most precise astronomical observations. The construction of suchephemerides is highly constrained by the tracking observations, in particular range, of the spaceprobes collected by the tracking stations on the Earth. The present planetary ephemerides (DE,INPOP, EPM) are mainly based on such observations. However, the data used by the planetaryephemerides are not the direct raw tracking data, but measurements deduced after the analysisof raw data made by the space agencies and the access to such processed measurements remainsdifficult in terms of availability.The goal of the thesis is to use archives of past and present space missions data independentlyfrom the space agencies, and to provide data analysis tools for the improvement of theplanetary ephemerides INPOP, as well as to use improved ephemerides to perform tests ofphysics such as general relativity, solar corona studies, etc.The first part of the study deals with the analysis of the Mars Global Surveyor (MGS)tracking data as an academic case for understanding. The CNES orbit determination softwareGINS was used for such analysis. The tracking observations containing one-, two-, and threewayDoppler and two-way range are then used to reconstruct MGS orbit precisely and obtainedresults are consistent with those published in the literature. As a supplementary exploitationof MGS, we derived the solar corona model and estimated the average electron density alongthe line of sight separately for slow and fast wind regions. Estimated electron densities arecomparable with the one found in the literature. Fitting the planetary ephemerides, includingadditional data which were corrected for the solar corona perturbations, noticeably improves theextrapolation capability of the planetary ephemerides and the estimation of the asteroid masses(Verma et al., 2013a).The second part of the thesis deals with the complete analysis of the MESSENGER trackingdata. This analysis improved the Mercury ephemeris up to two order of magnitude comparedto any latest ephemerides. Such high precision ephemeris, INPOP13a, is then used to performgeneral relativity tests of PPN-formalism.[...]

When recent observational data and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some not-yet-understood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide a description of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize perturbations in the dark sector. In this thesis we discuss our new way of approaching this problem. We write down an effective action for linearized perturbations to the gravitational field equations for a given field content and use it to compute generalized gravitational field equations for linearized perturbations. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field content that is compatible with some assumed symmetry (which we take to be isotropy of the background spatial sections). After applying the formalism we obtain equations of state for dark sector perturbations, where the number of free parameters for wide classes of theories are identified.

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Dans ma thèse, je vais présenter une méthode que j'ai développée pour traiter les perturbations cosmologiques à l’ordre linéaire, appelée théorie des champs effective de l’énergie noire. Elle a l’avantage de quantifier les déviations du modèle ΛCDM d’une façon compacte et indépendante d’un choix de modèle spécifique. Dans un second temps, je parlerai de nouvelles théories que j'ai découvertes, qui vont au delà des théories d’Horndeski, que l’on pensait être les plus générales pour un système gravité + champ scalaire qui soit stable. En effet, j’expliquerai que les conditions habituelles qui sont requises pour qu’une théorie soit stable, i.e. que ses équations du mouvement ne possèdent pas de termes avec plus de deux dérivées, sont trop restrictives. Ensuite j’exposerai des travaux que j’ai menés sur les ondes gravitationnelles primordiales. Plus spécifiquement, j’expliquerai que les prédictions pour les modes tensoriels venant de l’inflation sont très robustes, contrairement aux modes scalaires. Cela implique en particulier que mesurer le spectre de puissance des ondes gravitationnelles donnerait directement accès à l’échelle d’énergie durant l’inflation. Je terminerai par une description de mon étude des relations de cohérence. Ce sont des relations entre les fonctions de corrélations des champs de densité cosmiques à n + 1 points et à n points, quand un des champs varie beaucoup plus lentement que les autres dans l’espace. Leur intérêt vient du fait que pour les dériver, nous n’avons presque pas besoin d’informations sur les champs qui varient rapidement : seulement que leurs conditions initiales sont gaussiennes, et qu’ils respectent le Principe d’Equivalence. / In this thesis, I will present a method I developped to treat cosmological perturbations at linear order, called the Effective Field Theory for Dark Energy (EFT of DE). It has the advantage of quantifying deviations from the standard model ΛCDM in compact and model independent manner. Secondly, I will discuss new theories that I discovered, that extend Horndeski theories, which were thought to be the most general theories to describe a system gravity + scalar that is stable. Indeed, I will argue that the usual conditions that are required for a theory to be stable, namely that its equations of motion are second-order in derivatives, are too restrictive. Then, I will show the work I did on primordial gravitationnal waves. More precisely, I will explain how the standard predictions for tensor modes coming from inflation are very robust, contrarily to the scalar ones. This implies in particular that measuring the power spectrum from gravitationnal waves would give a direct access to the energy scale of inflation. Finally, I will end by a description of my studies on consistency relations. These are relations between the n+1 and n correlations functions of the cosmic density fields when one of the fields varies much less than the others. They are interesting since the derivation needs very little information on the rapidly varying fields: only that their initial conditions are Gaussian and that they obey the Equivalence Principle.

Este trabalho visa o estudo das perturbações de sistemas gravitacionais altamente compactos, como buracos negros e estrelas de nêutrons e de quarks. As perturbações em questão podem ser de diversas naturezas (escalar, eletromagnética ou gravitacional), sendo que detivemo-nos mais atentamente naquelas de natureza gravitacional, pois estas têm despertado mais interesse por serem astronomicamente mais fáceis de detectar. Além de estudarmos tais perturbações, procedemos a uma comparação dos resultados para buracos negros, estrelas de nêutrons e de quarks. Tal comparação justifica-se pelo fato de que a confrontação de previsões teóricas com resultados experimentais pode ajudar-nos a identificar objetos astronômicos de interesse, distingüi-los e, no caso de estrelas, aprender algo sobre sua estrutura interna, particularmente sobre a equação de estado (EDE) do fluido estelar. No que se segue, dividimos o trabalho em sete partes. Em primeiro lugar, damos uma introdução bastante sucinta ao mesmo (Capítulo 1). Depois, falamos sobre a física de estrelas de nêutrons e de quarks (Capítulo 2). A seguir, fazemos um estudo comparativo dos dois tipos de estrelas (Capítulo 3). Mais adiante, discutimos as perturbações de diversos tipos, além de definir os MQNs (Modos Quasi-Normais) de buracos negros de Schwarzschild (Capítulo 4). Prosseguimos a discussão com a métrica de Reissner-Nordström-de Sitter (Capítulo 5) e introduzimos, na seqüência, os MQNs estelares, de forma muito breve (Capítulo 6). Por fim, apresentamos nossas conclusões (Capítulo 7). A parte inédita deste trabalho está concentrada nos capítulos 5 e 6, os quatro anteriores servindo de preparativo e de base comparativa para estes dois. / This work aims the detailed study of the perturbations of highly compact gravitational systems, such as black holes and both neutron and quark stars. Such perturbations may have several different characters, such as scalar and electromagnetic fields as well as gravitational (either axial or polar) disturbances. We have focused more closely on the latter kind of perturbation, since they offer better possibilities of detection in the near future, in the form of gravitational waves. Besides studying the aforementioned perturbations, we have proceeded to a comparison between black holes and neutron and quark stars , when it comes to the outcomes of the perturbations, usually called QNMs (quasi-normal modes). Such a comparison is actually in order, since a direct comparison of theoretical and observational data may help us identify astronomical objects and, in the case of compact stars, may provide valuable insights into these stars' inner structure, particularly when it comes to their equation of state (EOS). In what follows, we have subdivided this work in seven parts. We begin with a brief introduction (Chapter 1), then proceed to a description of the physics of both neutron and quark stars (Chapter 2) and, in the sequence, to a comparative study of both kinds of star (Chapter 3). Subsequently, we develop the perturbation theory of the Schwarzschild black holes, discussing their QNMs (Chapter 4) and doing the same, later, for a more general Reissner-Nordström-de Sitter geometry (chapter 5). After that, we provide a very brief introduction to the stellar MQNs (Chapter 6). Finally, we present our conclusions (Chapter 7). The chapters 5 and 6 carry the inedit part of this work, and the chapters from 1 to 4 pave the way and provide a comparative basis for them.

The purpose of this study was to see how the fundamental properties of hyperbolic geometry applies in physics.

Cette thèse présente les résultats de la recherche de signaux d'ondes gravitationnelles transitoires de longue durée dans les données des deux premiers runs d'observation des détecteurs advanced LIGO et advanced Virgo. Ces ondes sont principalement émises par des étoiles à neutrons ou des trous noirs impliqués dans des phénomènes violents. Pour certaines sources, une modélisation impliquant une dynamique complexe et des instabilités hydrodynamiques peut prédire grossièrement la forme d'onde. Mais de manière générale, seulement l'information approximative sur la durée et la bande de fréquence est utilisée pour définir les limites de l'espace des paramètres de la recherche. Une méthode d'analyse temps-fréquence robuste aux incertitudes de la modélisation des signaux a donc été développé. En combinant les données de deux détecteurs de façon cohérente, la méthode permet de différencier les signaux recherchés du bruit de fond non gaussien des détecteurs. En l'absence de détection, nous avons placé des limites supérieures sur l'énergie émise et le taux attendu pour ces sources. Une recherche du signal attendu après la fusion de deux étoiles à neutrons observé en août 2017 (GW170817) a également était faite dans l'hypothèse où une étoile à neutrons supre-massive a été formée. Aucun signal n'a été identifié et j'ai montré que des détecteurs un ordre de grandeur plus sensibles auraient été nécessaires pour détecter un tel signal. / This thesis shows the results of the search of long duration transient gravitational waves using the data from the first two observation runs of advanced LIGO and advanced Virgo detectors. These long duration gravitational waves are mainly emitted by neutrons stars or black hole involved in extreme phenomena. For some sources, a modeling involving a complex dynamics and hydrodynamic instabilities can predict roughly the waveform. Nevertheless, for the general case, only a partial informations on the duration and frequency band are used to limits the parameters space. A time-frequency analysis, sturdy enough to modeling incertitude, has been developed and applied to the data. Combining data from two detectors in a coherent way, the analysis can distinguish between signal and detector's non gaussian background noise. In the absence of detection, we have placed upper limits on the energy emitted and the expected rate for these sources. A search for the expected signal emitted by the object created after the neutron stars coalescence and merger observed in August 2017 (GW170817) was also made assuming a supra-massive neutron star was created and survived hundred of seconds after the merger. No signal has been found and we have shown that detectors of an order of magnitude more sensible would have been required to detect a signal from this source.

We report on recent advancement in the theory of light propagation in the Solar System aiming at sub-micro-arcsecond level of accuracy: (1) A solution for the light ray in 1.5PN approximation has been obtained in the field of N arbitrarily moving bodies of arbitrary shape, inner structure, oscillations, and rotational motion. (2) A solution for the light ray in 2PN approximation has been obtained in the field of one arbitrarily moving pointlike body.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21557号 / 理博第4464号 / 新制||理||1641(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 柴田 大, 教授 田中 貴浩, 教授 井岡 邦仁 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM