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arXiv · 1404.6226

Global stability analysis for cosmological models with non-minimally coupled scalar fields

Maria A. Skugoreva·Alexey V. Toporensky·Sergey Yu. Vernov
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Abstract

We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the $N$ degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n 2N$ cases. Some special features connected with the important cases of $N=n$ (including the quadratic potential with quadratic coupling) and $n=2N$ (which shares its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover the most interesting cases of small $N$ and $n$ by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global features of dynamics is also studied.

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Maria A. Skugoreva, Alexey V. Toporensky, Sergey Yu. Vernov. 2014-09-14. Global stability analysis for cosmological models with non-minimally coupled scalar fields. https://doi.org/10.1103/physrevd.90.064044

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