# On the Topology and Future Stability of the Universe

## Hans Ringström

### Abstract

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

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, matter is modelled using kinetic theory. As background material, the general theory of the Cauchy problem for the Einstein–Vlasov equations is therefore developed.

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

### Bibliographic Information

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

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

### Authors

#### Affiliations are at time of print publication.

Hans Ringström, *author*

Associate Professor, Department of Mathematics, KTH Royal Institute of Technology, Sweden

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