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

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.

21 pages, 9 figures, v2: references added, accepted for publication in PRD

References in corpus (19)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• The Standard Model Higgs boson as the inflaton
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Can dark energy evolve to the Phantom?
• Higgs inflation: consistency and generalisations
• Inflation scenario via the Standard Model Higgs boson and LHC
• Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields
• Higgs inflation still alive
• Dynamical analysis of generalized Galileon cosmology
• Cosmological dynamics of Scalar--Tensor Gravity
• Cosmology of the proxy theory to massive gravity
• The double attractor behavior of induced inflation
• Dark Energy, Induced Gravity and Broken Scale Invariance
• Reconstruction of Scalar Potentials in Modified Gravity Models

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• Classes of non-minimally coupled scalar fields in spatially curved FRW spacetimes
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Spontaneous symmetry breaking as a result of extra dimensions compactification
• From inflation to dark energy in scalar-tensor cosmology
• Study of Antigravity in an F(R) Model and in Brans-Dicke Theory with Cosmological Constant
• Integrable cosmological models with non-minimal coupling and bounce solutions