### Abstract

In this paper we assume the de Sitter space version of black hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter spaceshould be implemented. Then we prove a no go theorem for implementing the symmetries if the entropy is finite. Thus we must either give up the fmiteness of de Sitter spaceentropy or the exact symmetry of the classical space. Each has interesting implications for the very long time behavior. We argue that the lifetime of a de Sitter phase can not exceed the Poincaré recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.

Original language | English (US) |
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Pages (from-to) | 1325-1338 |

Number of pages | 14 |

Journal | Journal of High Energy Physics |

Volume | 7 |

Issue number | 7 |

State | Published - Jul 1 2003 |

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### Keywords

- AdS-CFT and dS-CFT Correspondence
- Black Holes in String Theory
- Space-Time symmetries
- Thermal Field Theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*7*(7), 1325-1338.