Stability analysis for non-minimally coupled dark energy models in the Palatini formalism

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Abstract

In this paper, we use the method of global analysis to study the stability of de-Sitter solutions in an universe dominated by a scalar field dark energy, which couples non-minimally with the Ricci scalar defined in the Palatini formalism. Effective potential and phase-space diagrams are introduced to describe qualitatively the de-Sitter solutions and their stabilities. We find that for the simple power-law function \(V(\varphi)=V_{0}\varphi^{n}\) there are no stable de-Sitter solutions. While for some more complicated potentials, i.e. \(V(\varphi)=V_{0}\varphi^{n}+\varLambda\) and \(V(\varphi)=V_{0} (e ^{-\lambda\varphi}+e^{\lambda\varphi})^{2}\), stable de-Sitter solutions can exist.

Keywords

Dark energy Scalar field Non-minimal coupling Palatini formalism 

Notes

Acknowledgements

We appreciate very much helpful comments and suggestions by an anonymous referee. This work was supported by the National Natural Science Foundation of China under Grants No. 11775077, No. 11435006, No. 11690034, and No. 11375092, and K.C. Wong Magna Fund in Ningbo University.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center of Nonlinear Science and Department of PhysicsNingbo UniversityNingboChina

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