We consider the consequences of the leading quartic corrections to the Einstein-Hilbert action of gravity at low energy. Using the equivalence between the scalar R-2 contribution and a scalar-tensor field theory, we analyze the possible ways of detecting the associated scalaron and suggest that short distance tests of gravity, and in particular future tests of Newton's law aboard satellites, would provide the best environment to detect such a modification of gravity. We also analyze the regimes for which the R2 theory would result as a low energy manifestation of putative high energy UV completions involving extra dimensions. In the four-dimensional N =3D 1 supergravity limit of such extra-dimensional models, the R-2 models would emerge from the stabilization of a nearly no-scale super field such as the ones associated to the Kahler modulus corresponding to the breathing mode of a six-dimensional compactification.

We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (delta g((u))(00))(n) at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.

The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular-averaged consistency relations for the matter density correlations. This allows one to write the (l + n) density correlation, with l large-scale linear wave numbers that are integrated over angles, and n fixed small-scale nonlinear wave numbers, in terms of the small-scale n-point density correlation and l prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help design analytical models of gravitational clustering.

Aims. We estimate the amplitude of the source-lens clustering bias and of the intrinsic-alignment bias of weak-lensing estimators of the two-point and three-point convergence and cosmic-shear correlation functions. Methods. We use a linear galaxy bias model for the galaxy-density correlations, as well as a linear intrinsic-alignment model. For the three-point and four-point density correlations, we use analytical or semi-analytical models, based on a hierarchical ansatz or a combination of one-loop perturbation theory with a halo model. Results. For two-point statistics, we find that the source-lens clustering bias is typically several orders of magnitude below the weak-lensing signal, except when we correlate a very low-redshift galaxy (z(2) less than or similar to 0.05) with a higher redshift galaxy (z(1) greater than or similar to 0.5), where it can reach 10% of the signal for the shear. For three-point statistics, the source-lens clustering bias is typically on the order of 10% of the signal, as soon as the three galaxy source redshifts are not identical. The intrinsic-alignment bias is typically about 10% of the signal for both two-point and three-point statistics. Thus, both source-lens clustering bias and intrinsic-alignment bias must be taken into account for three-point estimators aiming at a better than 10% accuracy.

We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo model, we study the convergence rate of several perturbative expansion schemes and the impact of nonperturbative effects, as well as the sensitivity to phenomeno-logical halo parameters. We check that the simple reorganization of the standard perturbative expansion, with a Gaussian damping prefactor, provides a well-ordered convergence and a finite correlation function that yields a percent accuracy at the baryon acoustic oscillation peak (as soon as one goes to second order). Lagrangian-space expansions are somewhat more efficient, when truncated at low orders, but may diverge at high orders. We find that whereas the uncertainty on the halo-profile mass-concentration relation is not a strong limitation, the uncertainty on the halo mass function can severely limit the accuracy of theoretical predictions for P(k) (this also applies to the power spectra measured in numerical simulations). The real-space correlation function provides a better separation between perturbative and nonperturbative effects, which are restricted to x less than or similar to 10h(-1) Mpc at all redshifts.

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its n-point correlations. In the same limit, we derive the n-point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.

We investigate whether the late-time (at z <=3D 100) velocity dispersion expected in warm dark matter scenarios could have some effect on the cosmic web (i.e., outside of virialized halos). We consider effective hydrodynamical equations, with a pressurelike term that agrees at the linear level with the analysis of the Vlasov equation. Then, using analytical methods, based on perturbative expansions and the spherical dynamics, we investigate the impact of this term for a 1 keV dark matter particle. We find that the late-time velocity dispersion has a negligible effect on the power spectrum on perturbative scales and on the halo mass function. However, it has a significant impact on the probability distribution function of the density contrast at z similar to 3 on scales smaller than 0: 1h(-1) Mpc, which correspond to Lyman-alpha clouds. Finally, we note that numerical simulations should start at z(i) >=3D 100 rather than z(i) <=3D 50 to avoid underestimating gravitational clustering at low redshifts.

We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length x. This also gives the velocity structure functions. Next, for the case where the initial density is uniform, we obtain the distribution of the density, over any scale x, and we derive the density two-point correlation and power spectrum. Finally, we consider the Lagrangian displacement field and we derive the distribution of increments of the Lagrangian map. We check that this gives back the well-known mass function of shocks. For all distributions we describe the limiting scaling functions that are obtained in the large-scale and small-scale limits. We also discuss how these results generalize to other initial conditions, or to higher dimensions, and make the connection with a heuristic multifractal formalism. We note that the formation of point-like masses generically leads to a universal small-scale scaling for the density distribution, which is known as the "stable-clustering ansatz" in the cosmological context (where the Burgers dynamics is also known as the "adhesion model").

Weak gravitational lensing is responsible for the shearing and magnification of the images of high-redshift sources due to the presence of intervening mass. Since the lensing effects arise from deflections of the light rays due to fluctuations of the gravitational potential, they can be directly related to the underlying density field of the large-scale structures. Weak gravitational surveys are complementary to both galaxy surveys and cosmic microwave background observations as they probe unbiased nonlinear matter power spectra at medium redshift. Ongoing CMBR experiments such as WMAP and a future Planck satellite mission will measure the standard cosmological parameters with unprecedented accuracy. The focus of attention will then shift to understanding the nature of dark matter and vacuum energy: several recent studies suggest that lensing is the best method for constraining the dark energy equation of state. During the next 5 year period, ongoing and future weak lensing surveys such as the Joint Dark Energy Mission (JDEM; e.g. SNAP) or the Large-aperture Synoptic Survey Telescope will play a major role in advancing our understanding of the universe in this direction. In this review article, we describe various aspects of probing the matter power spectrum and the bi-spectrum and other related statistics with weak lensing surveys. This can be used to probe the background dynamics of the universe as well as the nature of dark matter and dark energy.