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.

Much of the recent progress in cosmology has come from studying the power spectrum of the cosmic microwave background (CMB). The latest results from the Planck satellite confirmed that the inflationary paradigm with the $\Lambda$CDM six-parameter model provides a very good description of the observed structures in the Universe. Even so, additional parameters, such as cosmic defects, are still allowed by current observational data. Additionally, many of the inflationary models predict a significant departure from Gaussianity in the distribution of primordial perturbations. Higher order statistics, such as the bispectrum, are required to test and constrain such models. The late-time distribution of matter in the Universe - large-scale structure (LSS) - contains much more information than the CMB that has not yet been used. In this thesis, we look at both problems: the effects of cosmic defects, in particular cosmic strings and domain walls on the CMB power spectrum through numerical simulations, and the dark matter bispectrum of large-scale structure. Topological defects are predicted by most inflationary theories involving symmetry breaking in the early Universe. In this thesis we study the effects of cosmic strings and domain walls on the CMB by determining their power spectrum. We use Nambu-Goto and field theory simulations for cosmic strings and domain walls respectively, and we determine the power spectra they produce with a modified Einstein-Boltzmann solver sourced by unequal time correlators from components of the energy-momentum tensor of the defects. We use these spectra together with CMB likelihoods to obtain constraints on the energy scales of formation of the cosmic defects, finding $G\mu/c^{2} < 1.29 \times 10^{−7}$ and $\eta < 0.93$ MeV (at 95% confidence level) for cosmic strings and domain walls respectively, when using the Planck satellite likelihoods. For the matter bispectrum of LSS, we compare different perturbative and phenomenological models with measurements from $N$-body simulations by using shape and amplitude correlators and we determine on which scales and for which redshifts they are accurate. We propose a phenomenological ‘three-shape’ model, based on the fundamental shapes we have observed by studying the halo model that are also present in the simulations. When calibrated on the simulations, this model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum HALOFIT-like methodology that could be used to describe and test parameter dependencies.

Depuis sa découverte en 1964, l’étude du Fond Diffus Cosmologique dans le domaine des longueurs d’ondes millimétriques est devenue un enjeu majeur de la recherche expérimentale dans le domaine de la cosmologie. En particulier, ses anisotropies en température, mesurées pour la première fois par le satellite COBE puis plus finement par l’expérience WMAP et le satellite PLANCK. L’existence prédite d’anisotropies de polarisation du Fond Diffus Cosmologique est fait actuellement parti du champ d’expérimentation privilégié de l’étude du CMB. En effet, la preuve d’existence des modes B de polarisation, signature unique des ondes gravitationnelles primordiales, fait actuellement l’objet d’une recherche expérimentale intensive par le biais notamment de l’instrument BICEP2 qui aurait détecté sa signature en 2014 dans des valeurs du rapport tenseur sur scalaire r = 0,2. Le projet QUBIC fait parti de ces expériences destinées à révéler les modes B de polarisation grâce à son instrument basé sur la technique des interféromètres et sur le développement de matrice de bolomètres, demandant un champ d’investigation poussé englobant, entre autre, la physique des solides, la physique des basses températures et la cosmologie. La thèse présentée ici se situe dans ce cadre, avec pour objectif l’élaboration d’une matrice de bolomètres dont la performance et l’optimisation devrait permettre d’acquérir la sensibilité nécessaire à l’observation des modes B de polarisation. Les différentes techniques expérimentales acquises au CSNSM d’Orsay permettent en effet d’envisager l’optimisation des éléments clé de la matrice de bolomètre en s’appuyant notamment sur l’alliage amorphe de NbxSi1-x pour l’élaboration d’un senseur thermique optimisé, et sur un matériau novateur, l’alliage de titane-vanadium, pour la mise au point d’un absorbeur de rayonnement supraconducteur efficace, dont la faible chaleur spécifique doit permettre d’atteindre un temps de réponse du détecteur de l’ordre de la dizaine de milliseconde, valeur du temps de réponse nécessaire à une lecture efficace du signal du Fond Diffus Cosmologique. Le manuscrit de thèse ici présent a pour ambition de développer les principes physiques nécessaires au champ d’investigation du travail à accomplir. Ainsi, cette étude propose d’élaborer les différents éléments d’un bolomètre, réunissant un senseur thermique optimisé ainsi qu’un absorbeur de rayonnement de faible chaleur spécifique, permettant d’envisager la mise au point d’une matrice de bolomètres optimisée dans le cadre du projet QUBIC dont la campagne d’observation est prévue courant 2015 au dôme C du pôle Sud. / Since its discovery in 1964, the study of the Cosmic Microwave Background (CMB) in the field as of millimetre-length wavelengths became a major stake of experimental research in the field of cosmology. In particular, its anisotropies in temperature, measured for the first time by satellite COBE then more finely by the experiment WMAP and the PLANCK satellite. The predicted existence of anisotropies of polarization of the Cosmic Microwave Background is currently been part of the privileged field of experimentation of the study of the CMB. Indeed, the proof of exists modes B of polarization, single signature of the paramount gravitational waves, currently is the object of an intensive experimental research by the means in particular of the instrument BICEP2 which would have detected its signature in 2014 in values of the tensor report on scalar R = 0.2. Project QUBIC makes party of these experiments intended to reveal the modes B of polarization thanks to its instrument based on the technique of the interferometers and the development of bolometers array, asking for a thorough field of investigation including, amongst other things, the solid state physics, the physics of the low temperatures and cosmology. The thesis presented here is within this framework, with for objective making of a bolometers array whose performance and optimization should make it possible to acquire the necessary sensitivity to the observation of the B-mode polarization. The various experimental techniques acquired with the CSNSM of Orsay indeed make it possible to consider the optimization of the key elements of the bolometers array while being pressed in particular on amorphous alloy of NbxSi1-x for making of an optimized thermal sensor, and on an innovative material, titanium-vanadium alloy, for the clarification of an effective superconducting absorber of radiation, whose low specific heat must make it possible to reach a response time of the detector about ten millisecond, value of the response time necessary to an effective reading of the signal of the Cosmic Microwave Background. The manuscript of thesis here present has as an ambition to develop the physical principles necessary to the field of investigation of work to be achieved. Thus, this study proposes to work out the various elements of a bolometer, joining together a thermal sensor optimized as well as an absorber of radiation of low specific heat, making it possible to consider the clarification of a bolometers array optimized within the framework of the project QUBIC whose observation campaign is envisaged during 2015 with the dome C of the south pole.