Current Topics In Mathematical Cosmology

In this volume, current topics from classical large scale models to quantum gravity effects in the mathematical formulation of physically motivated cosmological theories are discussed. There are contributions dealing with topics such as the singularity theorem, the cosmic no-hair theorem and other results related to the big bang and the inflationary cosmological models. Also discussed are non-standard themes like field equations of order higher than 2, space-times of dimension different from 4, relating also to current generalizations of string theory, and some issues in quantum cosmology.

"It contains a large variety of approaches to different aspects of the subject and can therefore be a source of inspiration for further research".General Relativity and Gravitation, 1999

Cosmology is a subject of much scientific and philosophical interest, but accounts are usually either non-mathematical or fully relativistic. This book seeks to give readers a quantitative understanding of some important aspects of general relativistic cosmology starting only with mathematics and Newtonian ideas in physics. The book is concerned mainly with various models that have been proposed to explain the large-scale structure of the universe: the Friedmann models, steady-state models, and model universes involving pressure. Topics also covered include special relativity, red-shift magnitude relations, radio source counts, Olbers' paradox, horizons, and cosmological coincidences.

The nature of time has long puzzled physicists and philosophers. Time potentially has very fundamental yet unknown properties. In 1993 a new model of multi-dimensional time was found to relate closely to properties of the cosmological redshift. An international conference was subsequently convened in April 1996 to examine past, current and new concepts of time as they relate to physics and cosmology. These proceedings incorporate 34 reviews and contributed papers from the conference. The major reviews include observational properties of the redshift, alternative cosmologies, critical problems in cosmology, alternative viewpoints and problems in gravitation theory and particle physics, and new approaches to mathematical models of time. Professionals and students with an interest in cosmology and the structure of the universe will find that this book raises critical problems and explores challenging alternatives to classical viewpoints.

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

The first part is devoted to the topic of quantum gravity and string theories, mainly concerned with recent authoritative results in the study of discretizations in classical and quantum general relativity, non-commutative theories of gravity, (2+1)-dimensional supergravity, and Berezin description of Kaehler quotients. The field to particle transition problem is also considered. The second part deals with cosmology and black holes. Here, cosmological, inflationary, and braneworld scenarios are investigated. Moreover, some scalar field models for the dark matter content of the universe as well as new models of protostellar collapse and fragmentation are presented. This part includes also a study of de Sitter/Anti-de Sitter phase transition for black holes, an understanding of hairy black holes and an improvement of the no-hair theorem proof for the Proca field. The third part is devoted to exact solutions, in particular classical and quantum cosmological solutions in scalar-tensor theories. Additionally, a discussion about conformally flat axisymmetric spacetimes and some considerations on accelerated expansion in scalar-tensor theories are presented. Experimental and some mixed topics are included in the final part. Among them is an experimental foundation of nonlocality and superluminal signal velocity in photonic tunneling, a proposal for testing the weak equivalence principle for charged particles in space. Moreover, a possible new type of skewon field linked to Maxwell theory is also presented, and an authoritative discussion at the interface of quantum and gravitational realms.

This book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action. The author's purpose is to provide a standard reference to all work that has been published since the mid-1970s and to link this work together in a single conceptual framework and a single notational formalism. A working knowledge of basic general relativity is assumed. The book will be essential reading for researchers and postgraduate students in mathematics, theoretical physics, and astronomy interested in cosmic strings.