Dynamical Systems in Cosmology

Author： J. Wainwright; G. F. R. Ellis

Publisher： Cambridge University Press‎

Publication year： 2005

E-ISBN: 9780511821448

P-ISBN(Paperback): 9780521673525

Subject： P159 cosmology

Keyword：恒星天文学、星系天文学、宇宙学

Language： ENG

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Dynamical Systems in Cosmology

Description

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.

Chapter

1 Geometry of cosmological models

1.1 Cosmological models

1.2 Symmetries of space-time

1.3 Evolution and constraint equations

1.4 Orthonormal frame formalism

1.5 Bianchi cosmologies

1.6 G2 cosmologies

2 Friedmann-Lemaitre universes

2.1 Basic properties and special solutions

2.2 Observational parameters

2.3 Qualitative analysis

2.4 Universes close to Friedmann-Lemaitre

3 Cosmological observations

3.1 Observations of discrete sources

3.2 The cosmic microwave background radiation

3.3 Big-bang nucleosynthesis (BBN)

3.4 Is the universe close to FL?

3.5 The best-fit FL parameters and the age problem

4 Introduction to dynamical systems

4.1 Differential equations and flows

4.2 Orbits and invariant sets

4.3 Behaviour near equilibrium points

4.4 Asymptotic evolution and intermediate evolution

Part two: Spatially homogeneous cosmologies

5 Qualitative analysis of Bianchi cosmologies

5.1 Overview

5.2 Expansion-normalized variables

5.3 Cosmological dynamical systems

6 Bianchi cosmologies: non-tilted class A models

6.1 Evolution equations and state space

6.2 Stability of the equilibrium points

6.3 Asymptotically self-similar models

6.4 The Kasner map and the Mixmaster attractor

6.5 Summary

7 Bianchi cosmologies: non-tilted class B models

7.1 The evolution equation and state space

7.2 Stability of the equilibrium points

7.3 Asymptotic and intermediate evolution

7.4 Summary

8 Bianchi cosmologies: extending the scope

8.1 The exceptional Bianchi VI٠ -1/9 models

8.2 Bianchi models with a two-fluid source

8.3 Cosmic 'no-hair' theorems for Bianchi models

8.4 Tilted Bianchi models

8.5 Recollapsing models

8.6 Other source terms: limitations

9 Exact Bianchi cosmologies and state space

9.1 Self-similar perfect fluid and vacuum solutions

9.2 Evolving vacuum solutions

9.3 Evolving non-tilted perfect fluid solutions

9.4 The space of initial data

10 Hamiltonian cosmology

10.1 The Hamiltonian formulation of Einstein's equations

10.2 Relationship with the orthonormal frame approach

10.3 Qualitative Hamiltonian cosmology

11 Deterministic chaos and Bianchi cosmologies

11.1 Chaotic dynamical systems

11.2 The metric approach

11.3 Hamiltonian method

11.4 Expansion-normalized variables

11.5 Summary

Part three: Inhomogeneous cosmologies

12 G2 cosmologies

12.1 Evolution equations

12.2 Equilibrium points: self-similar models

12.3 Evolving models: the separable class

12.4 G2 cosmologies and their specializations

12.5 Summary

13 Silent universes

13.1 Basic equations for silent universes

13.2 Dynamical systems analysis

13.3 Physical implications

13.4 Summary

14 Cosmological density perturbations

14.1 The geometrical approach to density perturbations

14.2 Perturbations of FL universes

14.3 Perturbations of Bianchi I universes

14.4 Summary

Part four: Conclusion

15 Overview

15.1 Cosmological dynamical systems

15.2 Bianchi universes and observations

15.3 Inhomogeneous cosmologies

References

Subject index

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