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We use cosmography to present constraints on the kinematics of the Universe without postulating any underlying theoretical model a priori. To this end, we use a Markov Chain Monte Carlo analysis to perform comparisons to the supernova Ia…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
We review dark energy models which can present non-negligible fluctuations on scales smaller than Hubble radius. Both linear and nonlinear evolutions of dark energy fluctuations are discussed. The linear evolution has a well-established…
The standard perturbation theory (SPT) approach to gravitational clustering is based on a fluid approximation of the underlying Vlasov-Poisson dynamics, taking only the zeroth and first cumulant of the phase-space distribution function into…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…
Cosmological perturbation theory provides the fundamental framework for describing the evolution of the matter-energy density field in an expanding Universe and serves as the basis for understanding the formation of large-scale structures…
We study the possibility to extract model independent information about the dynamics of the universe by using Cosmography. We intend to explore it systematically, to learn about its limitations and its real possibilities. Here we are…
We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and…
We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the…
An approximate statistical description of the formation and evolution of structure of the universe based on the Zel'dovich theory of gravitational instability is proposed. It is found that the evolution of DM structure shows features of…
A mathematical model is constructed for the evolution of spherical perturbations in a cosmological one-component statistical system of completely degenerate scalarly charged fermions with a scalar Higgs interaction. A complete system of…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
In the last dozens of years different data sets revealed the accelerated expansion of the Universe which is driven by the so called dark energy, that now dominates the total amount of matter-energy in the Universe. In a recent paper Glavan,…
Cross-correlation between the CMB and large-scale structure is a powerful probe of dark-energy and gravity on the largest physical scales. We introduce a novel estimator, the CMB-velocity correlation, that has most of his power on large…
The $\Lambda$CDM framework offers a remarkably good description of our universe with a very small number of free parameters, which can be determined with high accuracy from currently available data. However, this does not mean that the…
The dissipation of small-scale perturbations in the early universe produces a distortion in the blackbody spectrum of cosmic microwave background photons. In this work, we propose to use these distortions as a probe of the microphysics of…
In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial…
The latest cosmological observables analyses seem to converge to a concordant view of the cosmological model: namely the power law Lambda-CDM. The recent WMAP results comfort this new standard model. Nevertheless, some degeneracy in the CMB…