The trouble with de Sitter space

In this paper we assume the de Sitter Space version of Black HoleComplementarity which states that a single causal patch of de Sitter space isdescribed as an isolated finite temperature cavity bounded by a horizon whichallows no loss of information. We discuss the how the symmetries of de Sitterspace should be implemented. Then we prove a no go theorem for implementing thesymmetries if the entropy is finite. Thus we must either give up the finitenessof the de Sitter entropy or the exact symmetry of the classical space. Each hasinteresting implications for the very long time behavior. We argue that thelifetime of a de Sitter phase can not exceed the Poincare recurrence time. Thisis supported by recent results of Kachru, Kallosh, Linde and Trivedi.Comment: 15 pages, 1 figure. v2: added fifth section with comments on long time stability of de Sitter space, in which we argue that the lifetime can not exceed the Poincare recurrence time. v3: corrected a minor error in the appendi