Book contents
- Frontmatter
- Contents
- Preface
- Notation
- Part I Special Relativity
- Part II Riemannian geometry
- Part III Foundations of Einstein's theory of gravitation
- Part IV Linearized theory of gravitation, far fields and gravitational waves
- Part V Invariant characterization of exact solutions
- Part VI Gravitational collapse and black holes
- Part VII Cosmology
- 40 Robertson–Walker metrics and their properties
- 41 The dynamics of Robertson–Walker metrics and the Friedmann universes
- 42 Our universe as a Friedmann model
- 43 General cosmological models
- Bibliography
- Index
43 - General cosmological models
Published online by Cambridge University Press: 05 May 2010
- Frontmatter
- Contents
- Preface
- Notation
- Part I Special Relativity
- Part II Riemannian geometry
- Part III Foundations of Einstein's theory of gravitation
- Part IV Linearized theory of gravitation, far fields and gravitational waves
- Part V Invariant characterization of exact solutions
- Part VI Gravitational collapse and black holes
- Part VII Cosmology
- 40 Robertson–Walker metrics and their properties
- 41 The dynamics of Robertson–Walker metrics and the Friedmann universes
- 42 Our universe as a Friedmann model
- 43 General cosmological models
- Bibliography
- Index
Summary
What is a cosmological model?
A cosmological model is a model of our universe which, taking into account and using all known physical laws, predicts (approximately) correctly the observed properties of the universe, and in particular explains in detail the phenomena in the early universe. Such a model must also explain inter alia why the universe was so homogeneous and isotropic at the epoch of last scattering of the cosmic microwave background, and how and when inhomogeneities (galaxies and stars) arose.
In a more restricted sense cosmological models are exact solutions of the Einstein field equations for a perfect fluid that reproduce the important features of our universe. Because there is only one actual universe the large number of known or possible cosmological models may at first seem surprising. There are, however, two reasons for this multiplicity.
Firstly, only a section of our universe is known, both in space and in time. All cosmological models which differ only near the origin of the universe must be accepted for competition. In fact solutions are known which are initially inhomogeneous or anisotropic to a high degree, and which then increasingly come to approximate a Friedmann universe. All cosmological models which yield a redshift and a cosmic background radiation can hardly be refuted. The possibility cannot be excluded that our universe is not homogeneous and isotropic, but has those properties only approximately in our neighbourhood. An expanding ‘dust star’, that is, a section of a Friedmann universe which is surrounded externally by a static Schwarzschild metric (the model of a collapsing star discussed in Section 36.3), may also perhaps be an excellent model of the universe.
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- RelativityAn Introduction to Special and General Relativity, pp. 380 - 387Publisher: Cambridge University PressPrint publication year: 2004