京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18070号 / 理博第3948号 / 新制||理||1569(附属図書館) / 30928 / 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 佐々木 節, 教授 田中 貴浩, 教授 畑 浩之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Wir bewerten und vergleichen konkurrierende kosmologische Modelle im Hinblick auf theoretische Konsistenz und empirische Kohärenz. Ferner finden wir neue Wege, aktuelle kosmologische Paradigmen des frühen Universums weiter zu entwickeln. Im ersten Teil der Arbeit zeigen wir, dass die empirischen Daten der Planck2013-Satellitenmission für eine spezielle Klasse inflationärer Modelle sprechen, nämlich sog. “plateauartige Modelle mit schmalem Feldbereich”; gleichsam werden die einfachsten inflationären Modelle von den Messdaten nicht gestärkt. Wir formulieren eine neuartige konzeptionelle Schwierigkeit für Plateau-Modelle. Diese besteht darin, dass in einer Energielandschaft, die sowohl plateauartige als auch einfachere Formen der inflationären Potenziale enthält, die plateauartigen weniger Inflation produzieren und es deshalb weniger wahrscheinlich ist, dass sie das observable Universum beschreiben. Wir zeigen ferner, dass dieselben Plateau-Modelle mit einem neuen Multiversumsproblem und einem neuen Anfangswertsproblem behaftet sind. Im zweiten Teil untersuchen wir die Implikationen einer einfachen und experimentell motivierten Zusatzbedingung, Skalenfreiheit. Wir zeigen, dass die uneingeschränkte Palette inflationärer Potenziale sich auf ein wohldefiniertes Bündel inflationärer Modelle reduziert. Dabei verwenden wir eine allgemeine hydrodynamische Beschreibung. Wir klassifizieren und bewerten diese skalenfreien inflationären Modelle im Licht von Planck2013. Anschließend wiederholen wir die Analyse, um ähnliche skalenfreie zyklische Modelle des Universums zu konstruieren. Diese Modelle vergleichen wir mit unseren Ergebnissen, die wir für die skalenfreie inflationäre Theorie gewonnen haben. Im dritten Teil der Arbeit führen wir eine neue Klasse stabiler zyklischer Modelle ein. Wir zeigen, dass diese Modelle weniger Feinabstimmung der Anfangswerte benötigen. Gleichsam generieren sie vernachlässigbare Nicht-Gaussianität in Übereinstimmung mit den Planck2013-Messdaten. / In this thesis we evaluate and compare competing cosmological models for empirical and theoretical consistency and identify new ways of improving current paradigms of early universe cosmology. In the first part, we show that the most recent experimental data from the Planck2013 satellite measuring fluctuations in the cosmic microwave background favors a special class of “small-field plateau-like” models of inflation and disfavors the simplest inflationary potentials. We then identify a new kind of conceptual difficulty for the plateau models that we call the unlikeliness problem – namely, in an energy landscape that includes both plateau-like and simpler potential shapes, the plateau-like produces less inflation and, hence, is less likely to explain our observable universe. In addition, we show that the very same plateau-like models suffer from a new multiverse problem and a new initial conditions problem because they require that inflation starts at energy densities well below the Planck scale. Third, we comment on the impact of these results on the standard view of inflation and more recent versions of the theory invoking the multiverse and complex energy landscapes. In the second part of this thesis, imposing a single, simple, well-motivated constraint – scale-freeness – and using a general hydrodynamic analysis, we show that the unrestricted range of inflationary potentials reduces to a well-defined bundle of inflationary models. We classify and evaluate the scale-free inflationary models in light of Planck2013. We then repeat the construction to produce analogous scale-free bouncing cyclic models of the universe and compare with the inflationary results. In the third part, we introduce a new class of stable ekpyrotic/cyclic models that require less fine-tuning and generate negligible non-Gaussianity consistent with Planck2013 data.

In dieser Arbeit untersuchen wir kosmologische Modelle des frühen Universums, insbesondere alternative Modelle zur Inflationstheorie. Im ersten Teil leiten wir mithilfe des kovarianten Formalismus die Bewegunsgleichungen für zwei Skalarfelder mit nicht-kanonischem Feldraum bis zur dritten Ordnung in der Störtheorie her. Diese Gleichungen können dazu verwendet werden, Vorhersagen für die Bi- und Trispektren von Multi-Feldmodellen zu treffen, z.B. nicht-minimale ekpyrotische Modelle. In diesen Modellen werden zuerst aufgrund der nicht-minimalen kinetischen Kopplung zwischen den beiden Skalarfeldern nahezu skaleninvariante Entropiefluktuationen erzeugt, die dann anschließend in adiabatische Fluktuationen umgewandelt werden. Das Bi- sowie das Trispektrum der Entropiefluktuationen ist genau null während der ekpyrotischen Phase. Damit die Amplitude der adiabatischen Fluktuationen und das Bispektrum kompatibel mit derzeitigen Messungen sind, muss der Umwandlungsprozess effizient sein, was zu einem signifikanten, negativen Trispektrum-Parameter führt. Als zweite Alternative zur Inflation konstruieren wir ein neues kosmologisches Modell, das im Rahmen der Skalar-Tensor-Gravitationstheorien Elemente der Inflation mit Elementen des ekpyrotischen Modells verbindet. Während einer Phase der Konflation expandiert das Universum beschleunigt, jedoch mit negativer potentieller Energie. Skalare und tensorielle Fluktuationen werden nicht verstärkt – die ewige Inflation und die damit einhergehenden Unendlichkeiten werden vermieden. Wir zeigen außerdem, wie Dichtefluktuationen in Übereinstimmung mit aktuellen Beobachtungen erzeugt werden können, indem wir mithilfe eines zweiten Skalarfeldes den entropischen Mechanismus einsetzen. Beide Modelle unterscheiden sich von “slow-roll” Inflationstheorien basierend auf einem Skalarfeld darin, dass keine primordialen Gravitationswellen produziert werden und sie folglich mit den aktuellen Daten des PLANCK-Satelliten übereinstimmen. / In this thesis we explore cosmological models of the early universe, in particular alternatives to the theory of inflation. In the first part of this thesis, we derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory, employing the covariant formalism. These equations can be used to derive predictions for local bi- and trispectra of multi-field cosmological models, e.g. in non-minimal ekpyrotic models. In these models, nearly scale-invariant entropy perturbations are generated first due to a non-minimal kinetic coupling between two scalar fields, and subsequently converted into curvature perturbations. Remarkably, the entropy perturbations have vanishing bi- and trispectra during the ekpyrotic phase. However, in order to obtain a large enough amplitude and small enough bispectrum of the curvature perturbations, as seen in current measurements, the conversion process must be very efficient, leading to a significant, negative trispectrum parameter. As a second alternative to inflation, we construct a new kind of cosmological model that conflates inflation and ekpyrosis in the framework of scalar-tensor theories of gravity. During a phase of conflation, the universe undergoes accelerated expansion, but with negative potential energy. A distinguishing feature of the model is that it does not amplify adiabatic scalar and tensor fluctuations, and in particular does not lead to eternal inflation and the associated infinities. We also show how density fluctuations in accordance with current observations may be generated by adding a second scalar field to the model and making use of the entropic mechanism. The distinguishing observational feature of both models compared to single-field slow-roll inflation is an absence of primordial gravitational waves, in agreement with current data from the PLANCK satellite.

Dado un conjunto de datos, o una distribución, en un espacio de dimensión mayor a uno, las proyecciones aleatorias consisten en proyectar los datos, o calcular la marginal de la distribución, en un subespacio de menor dimensión que ha sido elegido de forma aleatoria. En nuestro caso de dimensión uno. En esta tesis presentamos dos aplicaciones de las proyecciones aleatorias. La primera es una definición de profundidad, que es computacionalmente efectiva, aproxima a la conocida profundidad de Tukey y es válida tanto en espacios multidimensionales como funcionales. La segunda es un test de Gaussianidad para procesos estrictamente estacionarios, que rechaza procesos no Gaussianos con marginal unidimensional Gaussiana. / A random projection consists in projecting a given data set, or in computing the marginal of a distribution, on a randomly chosen lower dimensional subspace. In our case, it is of dimension one.In this thesis, we present two applications of the random projections. The first one is a new definition of depth that is computationally effective, approximates the well-known Tukey depth and works as much in multidimensional spaces as in functional. The second is a test of Gaussianity for strictly stationary processes, which rejects non-Gaussian processes with Gaussian one-dimensional marginal.

In dieser Arbeit studieren wir das ekpyrotische Szenario, welches ein kosmologisches Modell des frühen Universums ist. Dieses Modell erklärt mit Hilfe einer kontrahierenden ekpyrotischen Phase die "Anfangsbedingungen" des Universums. Das bedeutet, dass der konventionelle "Urknall" durch einem Rückprall ersetzt wird. In dieser Arbeit versuchen wir Unstimmigkeiten zwischen den Vorhersagen der ekpyrotischen Modelle und den Messungen der Kosmologischen Hintergrundstrahlung des Planck Satelliten zu lösen. Den Planck Messungen zufolge sind die ursprünglichen adiabatischen Fluktuationen fast skaleninvariant und gaußverteilt. Während der ekpyrotischen Phase werden typischer Weise Flutuationen mit nicht-Gaußschen Korrekturen erzeugt. Wir schlagen zwei Ansätze vor, um diese Unstimmigkeit zu beheben. In dem nicht-minimalen entropischen Mechanismus werden fast skaleninvariante entropische Fluktuationen mit Hilfe einer nicht-minimalen kinetischen Kopplung zwischen zwei Skalarfeldern erzeugt. Wir werden zeigen, dass die nicht-Gaußschen Korrekturen während der ekpyrotischen Phase genau Null sind. Dies führt zu insgesamt kleinen nicht-Gaußschen Korrekturen nach der Umwandlung von entropischen zu adiabatischen Fluktuationen. Im Folgendem werden wir eine kinetische Umwandlung untersuchen, die nach einem nicht-singulären Rückprall stattfindet. Das Wachstum der entropischen Fluktuationen während des Rückpralls hat zur Folge, dass die möglichen nicht-Gaußschen Korrekturen, die zur Zeit der ekpyrotischen Phase erzeugt wurden, während des Rückpralls unterdrückt werden. Im letzten Teil der Arbeit gehen wir ein gravierendes Problem des inflationären Paradigmas an, welches "slow-roll eternal inflation" genannt wird. Wir schlagen ein Modell vor, das Ideen von Inflation und Ekpyrosis verbindet. Während der Konflation expandiert das Universum beschleunigt. Die adiabatischen Fluktuationen verhalten sich jedoch wie bei ekpyrotischen Modellen und wird "slow-roll eternal inflation" verhindert. / In this thesis, we study the ekpyrotic scenario, which is a cosmological model of the early universe. In this model the ``initial conditions'' of the universe are determined by a contracting ekpyrotic phase, which means that the conventional ``Big Bang'' is replaced by a bounce. The following thesis addresses the tension between ekpyrotic predictions and the observations of the Cosmic Microwave Background radiation by the Planck team. According to the Planck data, the primordial curvature fluctuations are nearly scale-invariant and Gaussian. However, during ekpyrosis, the fluctuations have typically sizable non-Gaussian signatures. In this thesis, we propose two approaches in order to resolve the tension with observations. In the non-minimal entropic mechanism, nearly scale-invariant entropy perturbations are created due to a non-minimal kinetic coupling between two scalar fields. We will show that the non-Gaussian corrections during ekpyrosis are precisely zero leading to overall small non-Gaussian signatures after the conversion process from entropy perturbations to curvature perturbations. In the following, we will consider a kinetic conversion phase, which takes place after a non-singular bounce. Due to the growth of entropy perturbations during the bounce phase, the possibly large non-Gaussian corrections created during the ekpyrotic phase become suppressed during the bounce. The last part of this thesis addresses a major problem of the inflationary paradigm: Due to large adiabatic fluctuations, slow-roll eternal inflation creates infinitely many physically distinct pocket universes. We propose a model in the framework of scalar-tensor theories, which conflated ideas of both inflation and ekpyrosis. During conflation, the universe undergoes accelerated expansion, but there are no large adiabatic fluctuations like during ekpyrosis resulting in the absence of slow-roll eternal inflation.

This PhD thesis, written in english, studies the non-Gaussianity (NG) of extragalactic foregrounds to the Cosmic Microwave Background (CMB), the latter being one of the golden observables of today's cosmology. In the last decade has emerged research for deviations of the CMB to the Gaussian law, as they would discriminate the models for the generation of primordial perturbations. However the CMB measurements, e.g. by the Planck satellite, are contaminated by several foregrounds. I studied in particular the extragalactic foregrounds which trace the large scale structure of the universe : radio and infrared point-sources and the thermal Sunyaev-Zel'dovich effect (tSZ). I hence describe the statistical tools to characterise a random field : the correlation functions, and their harmonic counterpart : the polyspectra. In particular the bispectrum is the lowest order indicator of NG, with the highest potential signal to noise ratio (SNR). I describe how it can be estimated on data, accounting for a potential mask (e.g. galactic), and propose a method to visualise the bispectrum, which is more adapted than the already existing ones. I then describe the covariance of a polyspectrum measurement, a method to generate non-Gaussian simulations, and how the statistic of a 3D field projects onto the sphere when integrating along the line-of-sight. I then describe the generation of density perturbations by the standard inflation model and their possible NG, how they yield the CMB anisotropies and grow to form the large scale structure of today's universe. To describe this large scale structure, I present the halo model and propose a diagrammatic method to compute the polyspectra of the galaxy density field and to have a simple and powerful representation of the involved terms. I then describe the foregrounds to the CMB, galactic as well as extragalactic. I briefly describe the physics of the thermal Sunyaev-Zel'dovich effect and how to describe its spatial distribution with the halo model. I then describe the extragalactic point-sources and present a prescription for the NG of clustered sources. For the Cosmic Infrared Background (CIB) I introduce a physical modeling with the halo model and the diagrammatic method. I compute numerically the 3D galaxy bispectrum and produce the first theoretical prediction of the CIB angular bispectrum. I show the contributions of the different terms and the temporal evolution of the galaxy bispectrum. For the CIB angular bispectrum, I show its different terms, its scale and configuration dependence, and how it varies with model parameters. By Fisher analysis, I show it allows very good constraints on these parameters, complementary to or better than those coming from the power spectrum. Finally, I describe my work on measuring NG. I first introduce an estimator for the amplitude of the CIB bispectrum, and show how to combine it with similar ones for radio sources and the CMB, for a joint constraint of the different sources of NG. I quantify the contamination of extragalactic point-sources to the estimation of primordial NG ; for Planck it is negligible for the central CMB frequencies. I then describe my measurement of the CIB bispectrum on Planck data ; it is very significantly detected at 217, 353 and 545 GHz with SNR ranging from 5.8 to 28.7. Its shape is consistent between frequencies, as well as the intrinsic amplitude of NG. Ultimately, I describe my measurement of the tSZ bispectrum, on simulations and on Compton parameter maps estimated by Planck, validating the robustness of the estimation thanks to realist foreground simulations. The tSZ bispectrum is very significantly detected with SNR~200. Its amplitude and its scale and configuration dependence are consistent with the projected map of detected clusters and tSZ simulations. Finally, this measurement allows to put a constraint on the cosmological parameters : sigma_8*(Omega_b/0.049)^0.35 = 0.74+/-0.04 in agreement with other tSZ statistics.

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Cette thèse, écrite en anglais, étudie la non-Gaussianité (NG) des avant-plans extragalactiques au fond de rayonnement fossile (FDC), celui-ci étant une des observables de choix de la cosmologie actuelle. Ces dernières années a émergé la recherche de déviations du FDC à la loi Gaussienne, car elles permettraient de discriminer les modèles de génération des perturbations primordiales. Cependant les mesures du FDC, e.g. par le satellite Planck, sont contaminées par différents avant-plans. J'ai étudié en particulier les avant-plans extragalactiques traçant la structure à grande échelle de l'univers: les sources ponctuelles radio et infrarouges et l'effet Sunyaev-Zel'dovich thermique (tSZ). Je décris donc les outils statistiques caractérisant un champ aléatoire : les fonctions de corrélations, et leur analogue harmonique : les polyspectres. En particulier le bispectre est l'indicateur de plus bas ordre de NG avec le plus fort rapport signal sur bruit (SNR) potentiel. Je décris comment il peut être estimé sur des données en tenant compte d'un masque (e.g. galactique), et propose une méthode de visualisation du bispectre plus adaptée que les préexistantes. Je décris ensuite la covariance d'une mesure de polyspectre, une méthode pour générer des simulations non-Gaussiennes, et comment la statistique d'un champ 3D se projette sur la sphère lors de l'intégration sur la ligne de visée. Je décris ensuite la genèse des perturbations de densité par l'inflation standard et leur possible NG, comment elles génèrent les anisotropies du FDC et croissent pour former la structure à grande échelle de l'univers actuel. Pour décrire cette dite structure, j'expose le modèle de halo et propose une méthode diagrammatique pour calculer les polyspectres du champ de densité des galaxies et avoir une représentation simple et puissante des termes impliqués. Puis je décris les avant-plans au FDC, tant galactiques que extragalactiques. J'expose la physique de l'effet tSZ et comment décrire sa distribution spatiale avec le modèle de halo. Puis je décris les sources extragalactiques et présente une prescription pour la NG de sources corrélées. Pour le fond diffus infrarouge (FDI) j'introduis une modélisation physique par le modèle de halo et la méthode diagrammatique. Je calcule numériquement le bispectre 3D des galaxies et obtiens la première prédiction du bispectre angulaire FDI. Je montre les différentes contributions et l'évolution temporelle du bispectre des galaxies. Pour le bispectre du FDI, je montre ses différents termes, sa dépendence en échelle et en configuration, et comment il varie avec les paramètres du modèle. Par analyse de Fisher, je montre qu'il apporte de fortes contraintes sur ces paramètres, complémentaires ou supérieures à celles venant du spectre. Enfin, je décris mon travail de mesure de la NG. J'introduis d'abord un estimateur pour l'amplitude du bispectre FDI, et montre comment le combiner avec de similaires pour les sources radio et le FDC, pour une contrainte jointe des différentes sources de NG. Je quantifie la contamination des sources ponctuelles à l'estimation de NG primordiale ; pour Planck elle est négligeable aux fréquences centrales du FDC. Je décris ensuite ma mesure du bispectre FDI sur les données Planck ; il est détecté très significativement à 217, 353 et 545 GHz, avec des SNR allant de 5.8 à 28.7. Sa forme est cohérente entre les différentes fréquences, de même que l'amplitude intrinsèque de NG. Enfin, je décris ma mesure du bispectre tSZ, sur des simulations et sur les cartes tSZ estimées par Planck, validant la robustesse de l'estimation via des simulations d'avant-plans. Le bispectre tSZ est détecté avec un SNR~200. Son amplitude et sa dépendence en échelle et en configuration sont cohérentes avec la carte des amas détectés et avec les simulations. Enfin, cette mesure place une contrainte sur les paramètres cosmologiques : sigma_8 (Omega_b/0.049)^0.35 = 0.74+/-0.04 en accord avec les autres statistiques tSZ. / This PhD thesis, written in english, studies the non-Gaussianity (NG) of extragalactic foregrounds to the Cosmic Microwave Background (CMB), the latter being one of the golden observables of today's cosmology. In the last decade has emerged research for deviations of the CMB to the Gaussian law, as they would discriminate the models for the generation of primordial perturbations. However the CMB measurements, e.g. by the Planck satellite, are contaminated by several foregrounds. I studied in particular the extragalactic foregrounds which trace the large scale structure of the universe : radio and infrared point-sources and the thermal Sunyaev-Zel'dovich effect (tSZ). I hence describe the statistical tools to characterise a random field : the correlation functions, and their harmonic counterpart : the polyspectra. In particular the bispectrum is the lowest order indicator of NG, with the highest potential signal to noise ratio (SNR). I describe how it can be estimated on data, accounting for a potential mask (e.g. galactic), and propose a method to visualise the bispectrum, which is more adapted than the already existing ones. I then describe the covariance of a polyspectrum measurement, a method to generate non-Gaussian simulations, and how the statistic of a 3D field projects onto the sphere when integrating along the line-of-sight. I then describe the generation of density perturbations by the standard inflation model and their possible NG, how they yield the CMB anisotropies and grow to form the large scale structure of today's universe. To describe this large scale structure, I present the halo model and propose a diagrammatic method to compute the polyspectra of the galaxy density field and to have a simple and powerful representation of the involved terms. I then describe the foregrounds to the CMB, galactic as well as extragalactic. I briefly describe the physics of the thermal Sunyaev-Zel'dovich effect and how to describe its spatial distribution with the halo model. I then describe the extragalactic point-sources and present a prescription for the NG of clustered sources. For the Cosmic Infrared Background (CIB) I introduce a physical modeling with the halo model and the diagrammatic method. I compute numerically the 3D galaxy bispectrum and produce the first theoretical prediction of the CIB angular bispectrum. I show the contributions of the different terms and the temporal evolution of the galaxy bispectrum. For the CIB angular bispectrum, I show its different terms, its scale and configuration dependence, and how it varies with model parameters. By Fisher analysis, I show it allows very good constraints on these parameters, complementary to or better than those coming from the power spectrum. Finally, I describe my work on measuring NG. I first introduce an estimator for the amplitude of the CIB bispectrum, and show how to combine it with similar ones for radio sources and the CMB, for a joint constraint of the different sources of NG. I quantify the contamination of extragalactic point-sources to the estimation of primordial NG ; for Planck it is negligible for the central CMB frequencies. I then describe my measurement of the CIB bispectrum on Planck data ; it is very significantly detected at 217, 353 and 545 GHz with SNR ranging from 5.8 to 28.7. Its shape is consistent between frequencies, as well as the intrinsic amplitude of NG. Ultimately, I describe my measurement of the tSZ bispectrum, on simulations and on Compton parameter maps estimated by Planck, validating the robustness of the estimation thanks to realist foreground simulations. The tSZ bispectrum is very significantly detected with SNR~200. Its amplitude and its scale and configuration dependence are consistent with the projected map of detected clusters and tSZ simulations. Finally, this measurement allows to put a constraint on the cosmological parameters : sigma_8*(Omega_b/0.049)^0.35 = 0.74+/-0.04 in agreement with other tSZ statistics.

This biomedical engineering thesis explores the opportunities and challenges of 2D+t contrast echocardiography for left ventricle functional analysis, both clinically and within a computer vision atlas-based deformable template model framework. A database was created for the experiments in this thesis, with 21 studies of contrast Dobutamine Stress Echo, in all 4 principal planes. The database includes clinical variables, human expert hand-traced myocardial contours and visual scoring. First the problem is studied from a clinical perspective. Quantification of endocardial global and local function using standard measures shows expected values and agreement with human expert visual scoring, but the results are less reliable for myocardial thickening. Next, the problem of segmenting the endocardium with a computer is posed in a standard landmark and atlas-based deformable template model framework. The underlying assumption is that these models can emulate human experts in terms of integrating previous knowledge about the anatomy and physiology with three sources of information from the image: texture, geometry and kinetics. Probabilistic atlases of contrast echocardiography are computed, while noting from histograms at selected anatomical locations that modelling texture with just mean intensity values may be too naive. Intensity analysis together with the clinical results above suggest that lack of external boundary definition may preclude this imaging technique for appropriate measuring of myocardial thickening, while endocardial boundary definition is appropriate for evaluation of wall motion. Geometry is presented in a Principal Component Analysis (PCA) context, highlighting issues about Gaussianity, the correlation and covariance matrices with respect to physiology, and analysing different measures of dimensionality. A popular extension of deformable models ---Active Appearance Models (AAMs)--- is then studied in depth. Contrary to common wisdom, it is contended that using a PCA texture space instead of a fixed atlas is detrimental to segmentation, and that PCA models are not convenient for texture modelling. To integrate kinetics, a novel spatio-temporal model of cardiac contours is proposed. The new explicit model does not require frame interpolation, and it is compared to previous implicit models in terms of approximation error when the shape vector changes from frame to frame or remains constant throughout the cardiac cycle. Finally, the 2D+t atlas-based deformable model segmentation problem is formulated and solved with a gradient descent approach. Experiments using the similarity transformation suggest that segmentation of the whole cardiac volume outperforms segmentation of individual frames. A relatively new approach ---the inverse compositional algorithm--- is shown to decrease running times of the classic Lucas-Kanade algorithm by a factor of 20 to 25, to values that are within real-time processing reach.