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

TL;DR

This paper conducts a comprehensive stability analysis of cosmological models with non-minimally coupled scalar fields, examining how different potential and coupling parameters influence the universe's dynamic behavior.

Contribution

It provides a global qualitative analysis of the dynamics of non-minimally coupled scalar field cosmologies, including special cases like Higgs inflation, across various parameter regimes.

Findings

Identification of three main dynamic regimes based on power indices N and n.

Analysis of special cases including N=n and n=2N.

Influence of the cosmological constant on global dynamics.

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 $n<N$, $N<n<2N$ and $n>2N$ 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.