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Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background
Joint Authors
Dănilă, Bogdan
Harko, Tiberiu
Mak, Man Kwong
Pantaragphong, Praiboon
Sabau, Sorin V.
Source
Advances in High Energy Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-10-26
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
We study the stability of the cosmological scalar field models by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory.
In this approach, we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a “second geometrization” and considering them as paths of a semispray.
By introducing a nonlinear connection and a Berwald-type connection associated with the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model.
We obtain all the relevant geometric quantities, and we formulate the condition for Jacobi stability in scalar field cosmologies.
We consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential.
The Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases.
We also investigate the stability of the phantom quintessence and tachyonic scalar field models, by lifting the first-order system to the tangent bundle.
It turns out that in the presence of a power law potential both of these models are Jacobi unstable during the entire cosmological evolution.
American Psychological Association (APA)
Dănilă, Bogdan& Harko, Tiberiu& Mak, Man Kwong& Pantaragphong, Praiboon& Sabau, Sorin V.. 2016. Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background. Advances in High Energy Physics،Vol. 2016, no. 2016, pp.1-26.
https://search.emarefa.net/detail/BIM-1095243
Modern Language Association (MLA)
Dănilă, Bogdan…[et al.]. Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background. Advances in High Energy Physics No. 2016 (2016), pp.1-26.
https://search.emarefa.net/detail/BIM-1095243
American Medical Association (AMA)
Dănilă, Bogdan& Harko, Tiberiu& Mak, Man Kwong& Pantaragphong, Praiboon& Sabau, Sorin V.. Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background. Advances in High Energy Physics. 2016. Vol. 2016, no. 2016, pp.1-26.
https://search.emarefa.net/detail/BIM-1095243
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095243