Probabilistic Spacetime is a simple generalization of the classical model of spa- cetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, na- mely those using the path integral. It is argued that this model might be used to restrict the precision of the geometry on small scales without postulating discrete structure; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.

The equivalence principle has proven to be central to theories of gravity, with General Relativity being the simplest and most elegant theory to embody the principle. Most alternative theories of gravity struggle to satisfy the principle and still be distinct from GR. Extensions of cosmological and quantum theories question the irrefutably of the equivalence at every scale. The possibility of an equivalence principle violation at galactic scales would be an exciting prospect. In this thesis, we will carefully examine the equivalence principle through the study of chameleon scalar-tensor theories, this will include solutions for hypothetical stars known as boson stars. Such theories find varied application, especially in cosmology, where they model dark energy and inflation. The AWE hypothesis, is an instance of this. It is a nonuniversally coupled model in which violations of the equivalence principle on galactic scales may be apparent. We investigate spherically symmetric and static solutions within the framework of this theory. The constraints obtained from galactic rotation curves results in values of the couplings that show no significant violation of the equivalence principle or values consistent with a theory of dark energy

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.

No description available.

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.

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.

Les méthodes standard de détection du fond gravitationnel stochastique reposent sur l'hypothèse simplificatrice selon laquelle sa distribution ainsi que celle du bruit des détecteurs sont Gaussiennes. Nous proposons dans cette thèse des méthodes améliorées de détection du fond gravitationnel stochastique qui tiennent compte explicitement du caractère non-Gaussien de ces distributions. En utilisant un développement d'Edgeworth, nous obtenons dans un premier temps une expression analytique pour la statistique du rapport de vraisemblance en présence d'une distribution non Gaussienne du fonds gravitationnel stochastique. Cette expression généralise l'expression habituelle lorsque le coefficient de symétrie et le coefficient d'aplatissement de la distribution du fond stochastique sont non nuls. Sur la base de simulations stochastiques pour différentes distributions symétriques présentant des queues plus épaisses que celles de la distribution Gaussienne, nous montrons par ailleurs que le 4eme cumulant peut-être estimé avec une précision acceptable lorsque le ratio signal à bruit est supérieur à 1%, ce qui devrait permettre d'apporter des contraintes supplémentaires intéressantes sur les valeurs de paramètres issus des modèles astrophysiques et cosmologiques. Dans un deuxième temps, nous cherchons à analyser l'impact sur les méthodes de détection du fond gravitationnel stochastique de déviations par rapport à la normalité dans la distribution du bruit des détecteurs. / The new generation of interferometers should allow us to detect stochastic gravitational wave backgrounds that are expected to arise from a large number of random, independent, unresolved events of astrophysical or cosmological origin. Most detection methods for gravitational waves are based upon the assumption of Gaussian gravitational wave stochastic background signals and noise processes. Our main objective is to improve the methods that can be used to detect gravitational backgrounds in the presence of non-Gaussian distributions. We first maintain the assumption of Gaussian noise distributions so as to better focus on the impact of deviations from normality of the signal distribution in the context of the standard cross-correlation detection statistic. Using a 4th-order Edgeworth expansion of the unknown density for the signal and noise distributions, we first derive an explicit expression for the non-Gaussian likelihood ratio statistic, which is obtained as a function of the variance, but also skewness and kurtosis of the unknown signal and noise distributions. We use numerical procedures to generate maximum likelihood estimates for the gravitational wave distribution parameters for a set of symmetric heavy-tailed distributions, and we find that the fourth cumulant can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 1%, which should be useful for analyzing the constraints on astrophysical and cosmological models. In a second step, we analyze the efficiency of the standard cross-correlation statistic in situations that also involve non-Gaussian noise distributions.