>Magister Scientiae - MSc / Next-generation surveys of the large-scale structure of the Universe will be of great importance in allowing us to extract invaluable information about the nature of the Universe and the physical laws that govern it, at a higher precision than previously possible. In particular, they will allow us to more closely study primordial non-Gaussianity, a feature which leaves an imprint on the power spectrum of galaxies on the ultra-large scales and which acts as a powerful probe of the physics of the early Universe. To investigate the extent to which upcoming surveys will be able to improve our knowledge of primordial non-Gaussianity, we perform a forecast to predict the observational constraints on local-type primordial non-Gaussianity, as well as an extension that includes a scale dependence. We study the constraining power of a multi-tracer approach, where information from different surveys is combined to help suppress cosmic variance and break parameter degeneracies. More specifically, we consider the combination of a 21cm intensity mapping survey with each of two different photometric galaxy surveys, and also examine the effect of including CMB lensing as an additional probe. The forecast constraint from a combination of SKA1, a Euclid-like (LSST-like) survey and a CMB Stage 4 lensing experiment is (fNL) ' 0:9 (1:4) which displays a factor of 2 improvement over the case without CMB lensing, indicating that the surveys considered are indeed complementary. The constraints on the running index of the scale-dependent model are forecast as (nNL) ' 0:12 (0:22) from the same combination of surveys.

Les prédictions d'inflation du spectre de puissance de la perturbation de la courbure ont déjà fait l’objet de vérification d’un excellent niveau, permettant à de nombreux modèles de rester compatibles avec les observations. Dans la présente thèse, nous avons étudié les corrélations de troisième ordre qui pourraient permettre de mieux distinguer les différents modèles d'inflation les uns des autres. Parmi toutes les extensions possibles du modèle standard d'inflation, nous avons choisi d'étudier des modèles de deux champs scalaires à termes cinétiques standards et à métrique des champs plat. La nouveauté introduite par ces modèles est la présence de la perturbation d'isocourbure. Son interaction avec la perturbation adiabatique hors de l'horizon produit des non-linéarités caractéristiques des modèles à plusieurs champs scalaires. Dans, ce contexte, nous avons établi la forme de la perturbation adiabatique et de la perturbation d'isocourbure invariant sous transformations de jauge en deuxième ordre. De plus, nous avons trouvé l'action de troisième ordre qui décrit leurs interactions. En outre, nous avons élaboré le formalisme des grandes longueurs d'onde afin d'obtenir une expression pour le paramètre de non-gaussiannité fNL en fonction du potentiel des champs. Nous avons ensuite, utilisé cette formule pour traiter analytiquement - avec l'hypothèse de slow-roll - des classes générales de potentiels et vérifier nos résultats numériquement par la théorie exacte. De là, nous avons pu tirer des conclusions générales concernant les propriétés de fNL, comme par exemple la dépendance de sa magnitude des caractéristiques du trajet des champs et de la perturbation d'isocourbure, ainsi que sa dépendance de la magnitude et de la taille relative des trois impulsions dont le corrélateur à trois points est fonction. / Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function.

The topic of this thesis is about cosmic inflations, including the early-universe inflation that seeds the initial inhomogeneities of our universe, and the late-time cosmic acceleration triggered by dark energy. The two inflationary epochs have now become part of the standard $\Lambda$CDM cosmological model. In the standard paradigm, dark energy is a cosmological constant or vacuum energy, while the early-universe inflation is driven by a slowly rolling scalar field. Currently the minimal $\Lambda$CDM model with six parameters agrees well with cosmological observations. If the greatest achievement of the last twenty golden years of cosmology is the $\Lambda$CDM model, the theme of future precision cosmology will be to search for deviations from the minimal $\Lambda$CDM paradigm. It is in fact expected that the upcoming breakthroughs of cosmology will be achieved by observing the subdominant anomalies, such as non-Gaussianities in the Cosmic Microwave Background map. The aim of this thesis is then to make theoretical predictions from models beyond $\Lambda$CDM, and confront them with cosmological observations. These models include: 1) a new dark energy parametrization based on quintessence models; 2) reconstructing early-universe inflationary trajectories, going beyond the slow-roll assumption; 3) non-Gaussian curvature fluctuations from preheating after the early-universe inflation; 4) infra-red cascading produced by particle production during inflation; 5) preheating after Modular inflation; 6) decaying cold dark matter. We update the cosmological data sets -- Cosmic Microwave Background, Type Ia supernova, weak gravitational lensing, galaxy power spectra, and Lyman-$\alpha$ forest -- to the most current catalog, and run Monte Carlo Markov Chain calculations to obtain the likelihood of parameters. We also simulate mock data to forecast future observational constraints.

The topic of this thesis is about cosmic inflations, including the early-universe inflation that seeds the initial inhomogeneities of our universe, and the late-time cosmic acceleration triggered by dark energy. The two inflationary epochs have now become part of the standard $\Lambda$CDM cosmological model. In the standard paradigm, dark energy is a cosmological constant or vacuum energy, while the early-universe inflation is driven by a slowly rolling scalar field. Currently the minimal $\Lambda$CDM model with six parameters agrees well with cosmological observations. If the greatest achievement of the last twenty golden years of cosmology is the $\Lambda$CDM model, the theme of future precision cosmology will be to search for deviations from the minimal $\Lambda$CDM paradigm. It is in fact expected that the upcoming breakthroughs of cosmology will be achieved by observing the subdominant anomalies, such as non-Gaussianities in the Cosmic Microwave Background map. The aim of this thesis is then to make theoretical predictions from models beyond $\Lambda$CDM, and confront them with cosmological observations. These models include: 1) a new dark energy parametrization based on quintessence models; 2) reconstructing early-universe inflationary trajectories, going beyond the slow-roll assumption; 3) non-Gaussian curvature fluctuations from preheating after the early-universe inflation; 4) infra-red cascading produced by particle production during inflation; 5) preheating after Modular inflation; 6) decaying cold dark matter. We update the cosmological data sets -- Cosmic Microwave Background, Type Ia supernova, weak gravitational lensing, galaxy power spectra, and Lyman-$\alpha$ forest -- to the most current catalog, and run Monte Carlo Markov Chain calculations to obtain the likelihood of parameters. We also simulate mock data to forecast future observational constraints.

Galaxy redshift surveys are powerful probes of cosmology. Yet, in order to fully exploit the information contained in galaxy surveys, we need to improve upon our understanding of the structure formation in the Universe. Galaxies are formed/observed at late times when the density field is no longer linear so that understanding non-linearities is essential. In this thesis, we show that, at high redshifts, we can accurately model the galaxy power spectrum in redshift space by using the standard cosmological perturbation theory. Going beyond the power spectrum, we can use the three-point function, or the bispectrum, to gain important information on the early universe as well as on the galaxy formation via measurements of primordial non-Gaussianity and galaxy bias. We show that the galaxy bispectrum is more sensitive to primordial non-Gaussianities than previously recognized, making high-redshift galaxy surveys a particularly potent probe of the physics of inflation. Weak lensing offers yet another way of probing cosmology. By cross correlating the angular position of galaxies with the shear measurement from galaxy lensing or CMB lensing, we also show that one can obtain the information on cosmological distance scale, the galaxy bias, and the primordial non Gaussianity from weak lensing method. / text

Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function.

In Space Situational Awareness (SSA), it is crucial to assess the uncertainty related to thestate vector of resident space objects (RSO). This uncertainty plays a fundamental role in, forexample, collision risk assessment and re-entry predictions. A realistic characterization of thisuncertainty is, therefore, necessary.The most common representation of orbital uncertainty is through a Gaussian (or normal)distribution. However, in the absence of new observations, the uncertainty grows over timeand the Gaussian representation is no longer valid under nonlinear dynamics like spacemechanics. This study evaluates the time when the uncertainty starts becoming non-Gaussianin nature. Different algorithms for evaluating the normality of a distribution were implemented andMonte Carlo tests were performed on them to assess their performance. Also, the distancesbetween distributions when they are propagated under linear and nonlinear algorithms werecomputed and compared to the results from the Monte Carlo statistics tests in order to predictthe time when the Gaussianity of the distribution breaks. Uncertainty propagation using StateTransition Tensors and Unscented Transform methods were also studied. Among theimplemented algorithms for evaluating the normality of a distribution, it was found thatRoyston’s method gives the best performance. It was also found that if the Normalized L 2distance between the linear and non-linear propagated distributions is greater than 95%, thenuncertainty starts to become non-Gaussian. In the best case scenario of unperturbed two-bodymotion, it is observed that the Gaussianity is preserved for at least three orbital periods in thecase of Low-Earth and Geostationary orbits when initial uncertainty corresponds to the meanprecision of the space debris catalog. If the initial variances are reduced, then Gaussianity ispreserved for a longer period of time. Time for which Gaussian assumption is valid on orbitaluncertainty is also dependent on the initial mean anomaly. Effect of coordinatestransformation on Gaussianity validity time is also analyzed by considering uncertainty inCartesian, Keplerian and Poincaré coordinate systems. This study can therefore be used to improve space debris cataloguing.

The cosmic microwave background (CMB) provides unprecedented details about the history of our universe and helps to establish the standard model in modern cosmology. With the ongoing and future CMB observations, higher precision can be achieved and novel windows will be opened for studying different phenomena. Non-Gaussianity is one of the most exciting effects which fascinate many cosmologists. While numerous alternative inflationary models predict detectable primordial non-Gaussianities generated during inflation, the single-field slow-roll inflation of the standard model is known to produce negligible non-Gaussianities. However, post-inflationary processes guarantee the generation of non-Gaussianities through the nonlinear evolution of our universe after inflation, regardless of the underlying inflationary theory. These non-Gaussianities not only may contaminate the potential primordial non-Gaussian signals, but also may offer independent tests for late-time physics (such as General Relativity). Therefore, it is of great interest to study them quantitatively. In this thesis, we will study the post-inflationary non-Gaussianities in two main aspects. First, we calculate the CMB bispectrum imprinted by the 2nd-order perturbations during recombination. We carry out a numerical calculation including all the dominant effects at recombination and separate them consistently from the late-time effects. We find that the recombination bispectrum is subdominant compared to the ISW-lensing bispectrum. Although the effect will not be detectable for the Planck mission, its signal-to-noise is large enough that they present themselves as systematics. Thus, it has to be taken into account in future experiments. Second, we formulate the lensing, redshift and time-delay effects through the Boltzmann equation. The new formalism allows us to explicitly list out all the approximations implied in the canonical remapping approach. In particular, we quantify the correction of the CMB temperature power spectrum from the lens-lens couplings and confirm that the correction is small.

Le fond diffus cosmologique (CMB) permet d'étudier la physique à l'oeuvre dans l'univers primordial.Ses anisotropies ont été mesurées récemment avec une haute précision par le satellite Planck. Ces mesures sont en accord avec les prédictions de l'inflation, la théorie décrivant une période d'expansion rapide et accélérée de l'univers primordial. Pour distinguer les différents modèles d'inflation, il est important de chercher des déviations de la distribution gaussienne des anisotropies du CMB, appelées non-gaussianités.Cette thèse est consacrée à l'étude, à la fois des points de vue observationnels et théoriques, des non-gaussianités du type bispectral (liées aux fonctions de corrélations à trois points), caractérisées par les paramètres d'amplitude fNL.Après une partie introductive sur le modèle standard de la cosmologie et la théorie des perturbations cosmologiques,la deuxième partie de ce manuscrit décrit la méthode de l'estimateur de bispectre binné, utilisée pour extraire de l'information sur les non-gaussianités à partir des mesures du CMB. Pour obtenir des informations sur l'univers primordial, les données doivent être nettoyées de la contamination dûe aux avant-plans galactiques. Nous vérifions les résultats au niveau du bispectre. Des modèles numériques de plusieurs avant-plans galactiques sont déterminés à partir des données de Planck. Ces modèles ont été utilisés dans des analyses des cartes de la température du CMB et du ciel brut, afin d'améliorer la détermination de la quantité de non-gaussianités primordiales.La troisième partie de ce manuscrit porte sur l'étude des non-gaussianités bispectrales produites dans des modèles d'inflation à deux champs avec des termes cinétiques standards. Il est important de mieux comprendre quelles régions de l'espace des modèles d'inflation ont été éliminées par les résultats de Planck.Nous appliquons une nouvelle expression de fNL au cas d'un potentiel somme et nous montrons qu'il est très difficile de satisfaire en même temps aux conditions permettant fNL grand et la contrainte observationnelle sur l'indice spectral ns. Pour le cas de la somme de deux potentiels monomiaux et d'une constante, nous montrons explicitement dans quelles régions de l'espace des paramètres cela est possible et comment construire un tel modèle. Finalement, nous utilisons la nouvelle expression pour fNL pour montrer que dans le cas du potentiel somme, les résultats analytiques restent valides au-delà de l'approximation de roulement lent. / A powerful probe of the physics at play in the early universe is the Cosmic Microwave Background(CMB). Its anisotropies have been measured recently with high precision by the Planck satellite. These measurements are in agreement with the predictions of inflation, a theory describing a period of fast and accelerated expansion in the early universe. To discriminate between the different inflation models, it is important to look for deviations from Gaussianity of the CMB anisotropies (i.e. non-Gaussianity). This thesis is devoted to the study of non-Gaussianity of the bispectral type (related to the three-point correlation functions) parametrized by its amplitude parameters fNL, both from the theoretical and observational points of view.After an introductory part on standard cosmology, the second part of the thesis describes the method of the binned bispectrum estimator, used to extract information about non-Gaussianity from CMB measurements.In order to recover information about the primordial universe, one has to clean observational data from the contamination caused by galactic foregrounds. We verify the results at the bispectral level. Numerical templates for the temperature bispectra of several galactic foregrounds are determined using data from the 2015 Planck release. These templates are then used to perform joint analyses on raw sky and CMB temperature data maps, to improve the determination of the amount of primordial non-Gaussianity. In the third part, the level of bispectral non-Gaussianity produced in two-field inflation models with standard kinetic terms is investigated using the long-wavelength formalism. It is important to better understand what regions of inflation model space have been ruled out by Planck. We apply a newly derived expression for fNL to the case of a sum potential and show that it is very difficult to satisfy simultaneously the conditions for a large fNL and the observational constraints on the spectral index ns. In the case of the sum of two monomial potentials and a constant we explicitly show in which small region of parameter space this is possible, and we show how to construct such a model. Finally, we also use the new expression for fNL to show that for the sum potential,the explicit expressions remain valid even beyond the slow-roll approximation.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18069号 / 理博第3947号 / 新制||理||1569(附属図書館) / 30927 / 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