Related papers: Lectures on Mathematical Cosmology
This is a review article for The Review of Particle Physics 2020 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the end of 2019. Topics included are Parametrizing the Universe;…
This is a review article for The Review of Particle Physics 2010 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2010. Topics included are Parametrizing the Universe;…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
I motivate and discuss some recent work on theories with varying constants, and consider some possible observational consequences and tests. Particular emphasis is given to models which can (almost) exactly mimic the predictions of standard…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
Sujets qui sont plus particulierement abordes dans ce cours: 1. Elements de cosmologie, l'Univers homogene Les principes cosmologiques et leurs verifications observationnelles Histoire thermique de l'Univers Inflation, motivations et…
In this expository article we describe the attempt of defining cosmological singularities and we discuss their meaning in classical and quantum cosmology.
This is a review of cosmological models prepared for the Pont d'Oye workshop on the origin of structure in the universe. The classes of models are discussed in turn, and then some of their uses are considered.
This article briefly summarizes the increasingly precise observational estimates of the cosmological parameters. After three years on the stump, the Lambda-CDM model is still the leading candidate. Although the Universe is expanding, our…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(\varphi)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting…
The purpose of the paper, of which this is part II, is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. Part II provides…
In these two lectures I will discuss some outstanding problems in the standard model of cosmology, concentrating on the physics that might be related to the title of this school, ``Searching for the totally unexpected in the LHC era.'' In…
For a few years now, cosmology has a standard model. By this term, we mean a consistent theoretical background which is at the same time simple and broad enough to offer coherent explanations for the vast majority of cosmological phenomena.…
Modern cosmology has created a tight link between particle physics / field theory and a wealth of new observational data on the structure of the Universe. These lecture notes focus on some of the most important aspects concerning the…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
This lecture is an introduction to cosmological tests with clusters of galaxies. Here I do not intend to provide a complete review of the subject, but rather to describe the basic procedures to set up the fitting machinery to constrain…
We discuss a number of fundamental aspects of modern cosmological concepts, from the phenomenological, observational, theoretical and epistemic points of view. We argue that the modern cosmology, despite a great advent, in particular in the…
This is a review article for The Review of Particle Physics 2014 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2014. Topics included are Parametrizing the Universe;…