Euclidean vacuum mode functions for a scalar field on open de Sitter space

Misao Sasaki, Takahiro Tanaka, Kazuhiro Yamamoto

Research output: Contribution to journalArticlepeer-review

118 Citations (Scopus)


Motivated by recent studies of the one-bubble inflationary universe scenario that predicts a low density, negative curvature universe, we investigate the Euclidean vacuum mode functions of a scalar field in a spatially open chart of de Sitter space which is foliated by hyperbolic time slices. When we consider the possibility of an open inflationary universe, we are faced with the problem of the initial condition for the quantum fluctuations of the inflaton field, because the inflationary era should not last too long to lose all information of the initial condition. In the one-bubble scenario, in which an open universe is created in an exponentially expanding false vacuum universe triggered by quantum decay of a false vacuum, it seems natural that the initial state is the de Sitter-invariant Euclidean vacuum. Here we present explicit expressions for the Euclidean vacuum mode functions in the open chart for a scalar field with arbitrary mass and curvature coupling.

Original languageEnglish
Pages (from-to)2979-2995
Number of pages17
JournalPhysical Review D
Issue number6
Publication statusPublished - 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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