Related papers: On the relativistic mass function and averaging in…
We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones…
We suggest how we can use the mass profile of galaxy clusters beyond their virial radius to measure their mass accretion rate, a key prediction of structure formation models. The mass profile can be estimated by applying the caustic…
The Sunyaev-Zel'dovich effect (SZE) provides a unique way to map the large-scale structure of the universe as traced by massive clusters of galaxies. As a spectral distortion of the cosmic microwave background, the SZE is insensitive to 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…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In gaussian theories of structure formation, the galaxy cluster abundance is an extremely sensitive probe of the density fluctuation power spectrum and of the density parameter, $\Omega$. We develop this theme by deriving and studying in…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. We review cosmological observations and discuss some of the issues regarding averaging. We present a precise definition of…
We quantitatively compare a particle implementation of the adhesion approximation to fully non--linear, numerical nbody simulations. Our primary tool, cross--correlation of nbody simulations with the adhesion approximation, indicates good…
We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG)…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
The Large Scale Structure in the galaxy distribution is investigated using The First Data Release of the Sloan Digital Sky Survey. Using the Minimal Spanning Tree technique we have extracted sets of filaments, of wall--like structures, of…
Over the past decades, General Relativity and the concordance $\Lambda$CDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their…
We use Enzo, a hybrid Eulerian AMR/N-body code including non-gravitational heating and cooling, to explore the morphology of the X-ray gas in clusters of galaxies and its evolution in current generation cosmological simulations. We employ…
The mass function of galaxies and clusters of galaxies can be derived observationally based on different types of observations. In this study we test if these observations can be combined to a consistent picture which is also in accord with…
A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
We present a general analytical procedure for computing the number density of voids with radius above a given value within the context of gravitational formation of the large scale structure of the universe out of Gaussian initial…
An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…