The subject of the book is the topology and future stability of models of the universe. In standard cosmology, the universe is assumed to be spatially homogeneous and isotropic. However, it is of interest to know whether perturbations of the corresponding initial data lead to similar solutions or not. This is the question of stability. It is also of interest to know what the limitations on the global topology imposed by observational constraints are. These are the topics addressed in the book. The theory underlying the discussion is the general theory of relativity. Moreover, in the book, matt ... More

*Keywords: *
cosmology,
stability,
universe,
topology,
kinetic theory,
general relativity,
cauchy problem

Print publication date: 2013 | Print ISBN-13: 9780199680290 |

Published to Oxford Scholarship Online: September 2013 | DOI:10.1093/acprof:oso/9780199680290.001.0001 |

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## Front Matter

## Part I Prologue

## Part II Introductory material

## Part III Background and basic constructions

## Part IV Function spaces, estimates

## Part V Local theory

## Part VI The Cauchy problem in general relativity

## Part VII Spatial homogeneity

## Part VIII Future global nonlinear stability

## End Matter

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A Examples of pathological behaviour of solutions to nonlinear wave equations

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B Quotients and universal covering spaces

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C Spatially homogeneous and isotropic metrics

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D Auxiliary computations in low regularity

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E The curvature of left invariant metrics

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F Comments concerning the Einstein–Boltzmann system

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References

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Index

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