Dynamical Systems In Cosmology

This authoritative volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example, 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory. Review: '... much more than the usual conference proceedings, it is not just a collection of articles but rather a collectively written monograph ... The exceptional character of the book is guaranteed by the fact that its authors combine theoretical dynamical investigations with observational data ... It does not often happen that scientific meetings and conferences give such concrete results as those presented in this monograph. I admire the determination and the quality of the editors' and authors' work which results in so valuable a book.' M. Szydlowski, Classical Quantum Gravity '... this book is an excellent and authoritative account of the dynamical evolution of relativistic cosmologies and as such I heartily recommend it to all researchers who wish to delve deeper into the subject.' David Wands, Contemporary Physics 'This book is an excellent introduction to the application of modern dynamical systems theory to the study of cosmological models, and is at an appropriate level for new graduate students.' Alan A. Coley, General Relativity and Gravitation 'It differs from many other collections written by several contributors by a very good homogeneity of the material, including one common reference list.' Zentralblatt MATH Table of Contents: List of contributors; Preface; 1. The geometry of cosmological models G. F. R. Ellis, S. T. C. Siklos and J. Wainwright; 2. Friedmann-Lemaitre universes G. F. R. Ellis and J. Wainwright; 3. Cosmological observations G. F. R. Ellis and J. Wainwright; 4. Introduction to dynamical systems R. Tavakol; 5. Qualitative analysis of Bianchi cosmologies G. F. R. Ellis, C. Uggla and J. Wainwright; 6. Bianchi cosmologies: non-tilted class A models J. Wainwright; 7. Bianchi cosmologies: non-tilted class B models C. G. Hewitt and J. Wainwright; 8. Bianchi cosmologies: extending the scope C. G. Hewitt, C. Uggla and J. Wainwright; 9. Exact Bianchi cosmologies and state space C. G. Hewitt, S. T. C. Siklos, C. Uggla and J. Wainwright; 10. Hamiltonian cosmology C. Uggla; 11. Deterministic chaos and Bianchi cosmologies D. W. Hobill; 12. G2 cosmologies C. G. Hewitt and J. Wainwright; 13. Silent universes M. Bruni, S. Matarrese and O. Pantano; 14. Cosmological density perturbations P. K. S. Dansby; 15. Overview G. F. R. Ellis and J. Wainwright; References; Index.