General theory of cosmological perturbations in open and closed universes from the Horndeski action

Our Universe is nearly spatially flat, but this does not mean that it is exactly spatially flat. In this paper we derive general quadratic actions for cosmological perturbations in non-flat models from the Horndeski theory. This allows us to study how the spatial curvature influences the behavior of...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Akama, Shingo, Kobayashi, Tsutomu
Format: Article
Language:English
Subjects:
Astronomical models
Curvature
Tensors
Universe
Online Access:Get full text
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Summary:Our Universe is nearly spatially flat, but this does not mean that it is exactly spatially flat. In this paper we derive general quadratic actions for cosmological perturbations in non-flat models from the Horndeski theory. This allows us to study how the spatial curvature influences the behavior of cosmological perturbations in the early universe described by some general scalar-tensor theory. We show that a tiny spatial curvature at the onset of inflation is unlikely to yield large (or \({\cal O}(1)\)) effects on the primordial spectra even if one modifies gravity. We also argue that non-singular cosmological solutions in the Horndeski theory are unstable in spatially open cases as well as in flat cases.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.01863