[en] The large-scale structure of the Universe and their statistical properties can reveal many aspects on the physics of the early Universe as well as on its matter and energy content during the cosmic history. The last couple of years has witnessed a rapid growth of results provided by gravitational lensing surveys which proved extremely powerful in mapping matter inhomogeneities at cosmological scales. Such surveys can be used not only to firmly established the existence of dark matter but also to test the existence of a significant dark energy thought to be responsible of the acceleration of the Universe

[en] The author aims at presenting the set of knowledge on which cosmologists rely to describe the most solid aspects of current cosmological models, the history of the Universe and the evolution of its large structures. After an introduction to modern cosmology (brief description of the thermal history of the Universe, the standard cosmological model and its missing portions), the author describes the homogeneous Universe by addressing the following issues: energy and matter, Universe expansion, cosmography, Universe content, elements of the Universe thermal history, the freeze out. Then, he proposes a statistical description of fields, analyses the development of gravitational instabilities (fluctuation increase in linear theory, Lagrangian approach, power spectrum of large structures of the Universe, the quasi linear regime and mode coupling effects, the highly non linear regime, the halo model). The next parts discuss metrics fluctuations which are crucial for observations (Hubble radius and horizon, Einstein equations, Boltzmann equation for photons), gravitational lenses (equations of lens effects in various contexts), discuss temperature anisotropies and background polarizations, and the origin of structures. Perspectives are also addressed in a last chapter. Appendices propose elements related to general relativity, quantum fields in cosmology, and scalar and spinned fields

[en] Mechanisms for the generation of primordial non-Gaussian metric fluctuations in the context of multiple-field inflation are reviewed. As long as kinetic terms remain canonical, it appears that nonlinear couplings inducing non-Gaussianities can be split into two types. The extension of the one-field results to multiple degrees of freedom leads to gravity-mediated couplings that are ubiquitous but generally modest. Multiple-field inflation offers however the possibility of generating non-gravity-mediated coupling in isocurvature directions that can eventually induce large non-Gaussianities in the metric fluctuations. The robustness of the predictions of such models is eventually examined in view of a case study derived from a high-energy physics construction.

[en] After having recalled the main recent advances in cosmology (establishment of large catalogues of galaxies, development of the use of the Cold Dark Matter model or CDM model, development of inflation theories, and detection of temperature fluctuations of the cosmological radiation background), this course addresses the issue of formation of large structures. The author first presents some elements of cosmology within the frame of a homogeneous universe: cosmological principles and cosmography, evolution of the expansion factor, present constraints on cosmological parameters, thermal history of the Universe, motivations and basic principle for inflation. Then, he addresses elements of cosmology within the frame of an inhomogeneous universe: fluctuation growth, background of a model with cold dark matter, other models. In the next part, the author addresses linear theories of gravitational dynamics: equation of evolution in phase space, jeans length, Newtonian approximation with a single flow, Eulerian description or Lagrangian description, fluctuation growth in linear theory, the Zel'dovich approximation, vorticity, validity range for the linear approximation. The next part addresses the spherical collapse (or towards a non-linear dynamics): Press and Schechter theory, cluster density to constrain the amplitude of the power spectrum. The next chapter deals with the quasi-linear regime and effects of mode coupling: general properties of the perturbative development, skewness as an effect of mode coupling, dependence on cosmological parameters, interpretation and filtering effect. The next chapters address the hierarchy of correlations in a quasi-linear regime, the application of statistical properties of observable quantities (catalogues of galaxies, two-dimensional catalogues, effects of gravitational lens), the evolution towards a highly non-linear regime (experimental data, self-similar solutions, linear-non-linear transform, hierarchical models, towards a unified theory for matter distribution and light distribution)

[en] The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact that such calculations can be mapped, for super-horizon scales, into those of a classical system, we express the expected correlation functions in terms of classical quantities, power spectra, Green functions, that can be easily computed in the long-wavelength limit. Explicit results are presented that extend those already known for a de Sitter background. In particular the expressions of the late time amplitude of bispectrum and trispectrum, as well as the whole high-order correlation structure, are given in terms of the expansion factor behavior. When compared to the case of a de Sitter background, power law inflation and chaotic inflation induced by a massive field are found to induce high order correlation functions the amplitudes of which are amplified by almost one order of magnitude. These results indicate that the dependence of the related non-Gaussian parameters — such as f_NL — on the wave-modes is at percent level

[en] We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small-angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the infinitesimal cross section of a light bundle in the optical limit, and maps galaxy intrinsic shapes into their angular images. The calculation is done in the Poisson gauge without a specific matter content, including vector and tensor perturbations generated at second order and taking account of the inhomogeneities of a fixed redshift source plane. Our final result is expressed in terms of spin-2 operators on the sphere and is valid on the full sky. Beside the well-known lens-lens and Born corrections that dominate on small angular scales, we find new nonlinear couplings. These are a purely general relativistic intrinsic contribution, a coupling between the gravitational potential at the source with the lens, couplings between the time delay with the lens and between two photon deflections, as well as nonlinear couplings due to the second-order vector and tensor components. The inhomogeneity in the redshift of the source induces a coupling between the photon redshift with the lens. All these corrections become important on large angular scales and should thus be included when computing higher-order observables such as the bispectrum, in full or partially full-sky surveys.

[en] The large-scale structure of the universe and its statistical properties can reveal many aspects of the physics of the early universe as well as of its matter content during the cosmic history. Numerous observations, based to a large extent on large-scale structure data, have given us a concordant picture of the energy and matter content in the universe. In view of these results the existence of dark matter has been firmly established although it still evades attempts at direct detection. An even more challenging puzzle is, however, yet to be explained. Indeed the model suggested by the observations is only viable with the presence of a 'dark energy', an ethereal energy associated with the cosmological vacuum, that would represent about two-thirds of the total energy density of the universe. Although strongly indicated by observations, the existence of this component is nonetheless very uncomfortable from a high-energy physics point of view. Its interpretation is a matter of far reaching debates. Indeed, the phenomenological manifestation of this component can be viewed as a geometrical property of large-scale gravity, or as the energy associated with the quantum field vacuum, or else as the manifestation of a new sort of cosmic fluid that would fill space and remain unclustered. Low redshift detailed examinations of the geometrical or clustering properties of the universe should in all cases help clarify the true nature of the dark energy. We present methods that can be used in the future for exploring the low redshift physical properties of the universe. Particular emphasis will be placed on the use of large-scale structure surveys and more specifically on weak lensing surveys that promise to be extremely powerful in exploring the large-scale mass distribution in the universe

[en] In dimension 2 and above, the Burgers dynamics, the so-called 'adhesion model' in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is defined by a 'geometrical model' associated with this Burgers velocity field and where the matter distribution is fully determined, at each time step, by geometrical constructions. Our investigations are based on a set of numerical experiments that make use of an improved algorithm, for which the geometrical constructions are efficient and robust. In this work we focus on Gaussian initial conditions with power-law power spectra of slope n in the range -3< n<1, where a self-similar evolution develops, and we compute the behavior of power spectra, density probability distributions and mass functions. As expected for such dynamics, the density power spectra show universal high-k tails that are governed by the formation of pointlike masses. The two other statistical indicators however show the same qualitative properties as those observed for 3D gravitational clustering. In particular, the mass functions obey a Press-Schechter like scaling up to a very good accuracy in 1D, and to a lesser extent in 2D. Our results suggest that the 'geometrical adhesion model', whose solution is fully known at all times, provides a precious tool to understand some of the statistical constructions frequently used to study the development of mass halos in gravitational clustering.

[en] We consider the effect of modified gravity on the growth of large-scale structures at second order in perturbation theory. We show that modified gravity models changing the linear growth rate of fluctuations are also bound to change, although mildly, the mode coupling amplitude in the density and reduced velocity fields. We present explicit formulae which describe this effect. We then focus on models of modified gravity involving a scalar field coupled to matter, in particular chameleons and dilatons, where it is shown that there exists a transition scale around which the existence of an extra scalar degree of freedom induces significant changes in the coupling properties of the cosmic fields. We obtain the amplitude of this effect for realistic dilaton models at the tree-order level for the bispectrum, finding them to be comparable in amplitude to those obtained in the DGP and f(R) models

[en] We explore extensions of hybrid inflationary models in the context of supersymmetric D-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple-field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bispectrum and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bispectra and trispectra of cosmic microwave background anisotropies to efficiently reduce their parameter space