Vacua and correlators in hyperbolic de Sitter space

Fotios V. Dimitrakopoulos, Laurens Kabir, Benjamin Mosk, Maulik Parikh, Jan Pieter van der Schaar

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Abstract: We study the power- and bi-spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one-parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch-Davies vacuum state. Selecting the Bunch-Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch-Davies state the hyperbolic de Sitter n-point correlation functions have to match the planar de Sitter n-point correlation functions. The expressions for the planar and hyperbolic Bunch-Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power- and bi-spectrum. For the bi-spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch-Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.

Original languageEnglish (US)
Article number95
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 19 2015


  • Cosmology of Theories beyond the SM
  • Effective field theories
  • Models of Quantum Gravity

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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