Cosmological dynamics in the model with nonminimal kinetic coupling

Cosmological dynamics has been considered for the FRW Universe filled with a scalar field phi with the kinetic coupling kG(mu nu)phi,(mu)phi,(nu) and the effective potential V (phi) = Vo phi(N). The influence of such potential on the dynamics of the model is found using the methods of the theory of dynamical systems. Two stable asymptotic regimes are obtained: one exists only for 0 2. It is also shown that realistic cosmological scenarios are possible in this model

Cosmological dynamics in the model with nonminimal kinetic coupling

Cosmological dynamics has been considered for the FRW Universe filled with a scalar field phi with the kinetic coupling kG(mu nu)phi,(mu)phi,(nu) and the effective potential V (phi) = Vo phi(N). The influence of such potential on the dynamics of the model is found using the methods of the theory of dynamical systems. Two stable asymptotic regimes are obtained: one exists only for 0 2. It is also shown that realistic cosmological scenarios are possible in this model

Bouncing solutions in f(T) gravity

© 2020, The Author(s). We consider certain aspects of cosmological dynamics of a spatially curved Universe in f(T) gravity. Local analysis allows us to find conditions for bounces and for static solutions; these conditions appear to be in general less restrictive than in general relativity. We also provide a global analysis of the corresponding cosmological dynamics in the cases when bounces and static configurations exist, by constructing phase diagrams. These diagrams indicate that the fate of a big contracting Universe is not altered significantly when bounces become possible, since they appear to be inaccessible by a sufficiently big Universe

Global stability analysis for cosmological models with nonminimally coupled scalar fields

We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaître-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 n2N 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. © 2014 American Physical Society

Dynamical features of scalar-torsion theories

We investigate the cosmological dynamics in teleparallel gravity with nonminimal coupling. We analytically extract several asymptotic solutions, and we numerically study the exact phase-space behavior. Comparing the obtained results with the corresponding behavior of nonminimal scalar-curvature theory, we find significant differences, such as the rare stability and the frequent presence of oscillatory behavior. © 2015 American Physical Society

Board of Trustees Meeting, October 24, 2002

The agendas for meetings of the Johnson County Community College Board of Trustee

Cosmology with nonminimal kinetic coupling and a power-law potential

We consider cosmological dynamics in the theory of gravity with the scalar field possessing a nonminimal kinetic coupling to gravity, κG μνφμφν, and the power-law potential V(φ)=V0φN. Using the dynamical system method, we analyze all possible asymptotical regimes of the model under investigation and show that for sloping potentials with 0<N<2 there exists a quasi-de Sitter asymptotic H=1/√9κ corresponding to an early inflationary Universe. In contrast to the standard inflationary scenario, the kinetic coupling inflation does not depend on a scalar field potential and is only determined by the coupling parameter κ. We obtain that there exist two different late-time asymptotical regimes. The first one leads to the usual powerlike cosmological evolution with H=1/3t, while the second one represents the late-time inflationary Universe with H=1/√3κ. This secondary inflationary phase depends only on κ and is a specific feature of the model with nonminimal kinetic coupling. Additionally, an asymptotical analysis shows that for the quadric potential with N=2, the asymptotical regimes remain qualitatively the same, while the kinetic coupling inflation is impossible for steep potentials with N>2. Using a numerical analysis, we also construct exact cosmological solutions and find initial conditions leading to the initial kinetic coupling inflation followed either by a "graceful" oscillatory exit or by the secondary inflation. © 2013 American Physical Society

Global stability analysis for cosmological models with nonminimally coupled scalar fields

We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaître-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 n2N 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. © 2014 American Physical Society