Related papers: A Large Deviation Principle at play in Large-Scale…

We investigate the properties of large--scale structure predicted in a class of mixed dark matter models in which the volatile component (made of particles with high rms velocity) derives from the decay of a heavier particle. Such models…

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution…

We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general…

The growth of large scale structure is studied in a universe containing both cold dark matter (CDM) and generalized Chaplygin gas (GCg). GCg is assumed to contribute only to the background evolution of the universe while the CDM component…

Explaining the formation and evolution of galaxies is one of the most challenging problems in observational cosmology. Many observations suggest that galaxies we see today could have evolved from the merging of smaller subsystems. Evolution…

Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

Even as our measurements of cosmological parameters improve, the physical nature of the dark sector of the universe largely remains a mystery. Many effects of dark sector models are most prominent at very large scales and will rely on…

The gravitational collapse of collisionless matter leads to shell-crossing singularities that challenge the applicability of standard perturbation theory. Here, we present the first fully perturbative approach in three dimensions by using…

A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we…

We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits…

These lectures deal with our current knowledge of the matter distribution in the universe, focusing on how this is studied via the large-scale structure seen in galaxy surveys. We first assemble the necessary basics needed to understand the…

We investigate how observations of strong lensing can be used to infer cosmological parameters, in particular the equation of state of dark energy. We focus on the growth of the critical lines of lensing clusters with the source redshift as…

We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…

We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the…

The evolution of two-point space correlation function of QSOs is analyzed in the framework of the theory of the large scale structure formation. For given cosmological models the agreement between theoretical predictions and observational…

In this work we study the simultaneous effect of primordial non-Gaussianity and the modification of the gravity in $f(R)$ framework on large scale structure observations. We show that non-Gaussianity and modified gravity introduce a scale…

If primordial fluctuation is Gaussian distributed, higher-order cumulants of the cosmic fields reflect nonlinear mode coupling and provide useful information of gravitational instability picture of structure formation. We show that their…

This paper studies large deviation principles and weak convergence, both at the level of finite-dimensional distributions and in functional form, for a class of continuous, isotropic, centered Gaussian random fields defined on the unit…

Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with…