Elliptic de Sitter space: DS/ℤ2

Maulik Parikh, Ivo Savonije, Erik Verlinde

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We propose that, for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an "elliptic" "Z 2 identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analogue of an S matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hubert space can be finite dimensional and still have a positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.

Original languageEnglish (US)
Article number064005
JournalPhysical Review D
Issue number6
StatePublished - 2003
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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