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.

Hybrid models of inflation are particularly interesting and well motivated, since easily embedded in various high energy frameworks like supersymmetry/supergravity, Grand Unified Theories or extra-dimensional theories. If the original hybrid model is often considered as disfavored, because it generically predicts a blue spectrum of scalar perturbations, realistic hybrid models can be in agreement with CMB observations. The dynamics of hybrid models is usually approximated by the evolution of a scalar field slowly rolling along a nearly flat valley. Inflation ends with a waterfall phase, due to a tachyonic instability. This final phase is usually assumed to be nearly instantaneous. <p> <p>In this thesis, we go beyond these approximations and analyze the exact 2-field non-linear dynamics of hybrid models. Several non trivial effects are put in evidence: 1) the possible violation of the slow-roll conditions along the valley induce the non existence of inflation at small field values. Provided super-planckian fields, the scalar spectrum of the original model is red, in agreement with CMB observations, independently of the position of the critical instability point. 2) Contrary to what was thought, the initial field values leading to inflation are not fine-tuned along the valley but also occupy a considerable part of the field space exterior to it. They form a complex connected structure with fractal boundaries that is the basin of attraction of the valley. Using bayesian methods, their distribution in the whole parameter space, including initial velocities, is studied. Natural bounds on the potential parameters are derived. 3) For the original model, after the field evolution along the valley, inflation continues for more than 60 e-folds along the waterfall trajectories in some part of the parameter space. Observable predictions are modified, and the scalar power spectrum of adiabatic perturbations is generically red, possibly in agreement with CMB observations. Moreover, topological defects are conveniently stretched outside the observable Universe. 4) The analysis of the initial conditions is extended to the case of a closed Universe, in which the initial singularity is replaced by a classical bounce. Contrary to some other scenarios, due to the attractor nature of the valley, the field values in the contracting phase do not need to be extremely fine-tuned to generate a bounce followed by a phase of hybrid inflation. <p> <p>In the third part of the thesis, we study how the present CMB constraints on the cosmological parameters could be ameliorated with the observation of the 21cm cosmic background from the dark ages and the reionization, by the future generation of giant radio-telescope. Assuming ideal foreground removals, forecasts on the cosmological parameters are determined for a characteristic Fast Fourier Transform Telescope experiment, by using both Fisher matrix and MCMC methods. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished