An overview of Cosmology

How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such...

I present a non-technical and necessarily biased and incomplete overview of our present understanding of the physical universe and its constituents, emphasizing what we have learned from the explosive growth in cosmological and astrophysical data acquisition and some of the key open questions that remain. The topics are organized under the labels space, time, and matter. Most bibliographical references are for the non-expert.

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 principe de base 2. Elements de cosmologie, l'Univers inhomogene La croissance des fluctuations Pourquoi un modele avec de la Matiere Noire Froide ? Evidences de l'existence de matiere noire 3. La dynamique gravitationnelle, les theories li...

These lectures describe how the Standard Model of cosmology ($\Lambda$CDM) has developped, based on observational facts but also on ideas formed in the context of the theory of fundamental interactions, both gravitational and nongravitational, the latter being described by the Standard Model of high energy physics. It focuses on the latest developments, in particular the precise knowledge of the early Universe provided by the observation of the Cosmic Microwave Background and...

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 and potentially powerful methods which may be used for future progress are also given from a unified perspective.

The current status of the theoretical and observational cosmology is reviewed.

I will review some results of observational cosmology which critically cast doubt upon the foundations of the standard cosmology: 1) The redshifts of the galaxies are due to the expansion of the Universe; 2) The cosmic microwave background radiation and its anisotropies come from the high energy primordial Universe; 3) The abundance pattern of the light elements is to be explained in terms of the primordial nucleosynthesis; 4) The formation and evolution of galaxies can only ...

We review the current standard model for the evolution of the Universe from an early inflationary epoch to the complex hierarchy of structure seen today. We summarize and provide key references for the following topics: observations of the expanding Universe; the hot early Universe and nucleosynthesis; theory and observations of the cosmic microwave background; Big Bang cosmology; inflation; dark matter and dark energy; theory of structure formation; the cold dark matter mode...

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 book chapter is to provide the reader with a concise introduction to both cosmology and dynamical system. The material is self-contained with references to more detailed work. It is aimed at applied mathematics and theoretical physics graduate...

What are the important unanswered questions in cosmology? The choice as to which are the most important is somewhat personal. In the view of the author, the ten topics chosen here for discussion must be included among the most fundamental. Present cosmological theory is unable to fully describe the evolution of the universe from the time of the Big Bang and a lack of observations makes it difficult to verify theoretical predictions. The questions posed here will only be answe...