Related papers: Statistical analysis of large-scale structure in t…
The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and…
I discuss and illustrate the development of large-scale structure in the Universe, emphasising in particular the physical processes and cosmological parameters that most influence the observationally accessible aspects of structure at large…
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological…
Subject of this article is the relationship between modern cosmology and fundamental physics, in particular general relativity as a theory of gravity on one side, together with its unique application in cosmology, and the formation of…
We investigate structure formation in a one dimensional model of a matter-dominated universe using a quasi-newtonian formulation. In addition to dark matter, luminous matter is introduced to examine the potential bias in the distributions.…
In this study, we explore the potential of utilizing the four Minkowski functionals, which can fully describe the morphological properties of the large-scale structures, as a robust tool for investigating the modified gravity, particularly…
The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and…
The purpose of these lectures is to give a short introduction into a very vast field of numerical simulations for cosmological applications. I focus on major features of the simulations: the equations, main numerical techniques, effects of…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
The morphology of galaxy clusters is quantified using Minkowski functionals, especially the vector-valued ones, which contain directional information and are related to curvature centroids. The asymmetry of clusters and the amount of their…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
The large amount of cosmological data already available (and in the near future) makes necessary the development of efficient numerical codes. Many software products have been implemented to perform cosmological analyses considering one or…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…