Cosmological dynamics of non-minimally coupled scalar field system and its late time cosmic relevance

We investigate the cosmological dynamics of non-minimally coupled scalar field system described by $F(\phi)R$ coupling with $F(\phi)=(1-\xi\phi^N)R$($N\ge2$) and the field potential, $V(\phi)=V_0\phi^n$. We use a generic set of dynamical variables to bring out new asymptotic regimes of the underlying dynamics. However, our dynamical variables miss the most important fixed point$-$ the de Sitter solution. We make use of the original form of system of equations to investigate the issues related to this important solution. In particular, we show that the de-Sitter solution which is a dynamical attractor of the system lies in the region of negative effective gravitational constant $G_N$ thereby leading to a ghost dominated universe in future and a transient quintessence(phantom) phase with $G_N>0$ around the present epoch (however, as demonstrated by Starobinsky in 1981, the ghost dominated universe, if exists, can not be accessed from the Universe we live in, we shall say more about this important result in the last section). We also carry out comparison of the model with other competing models of dark energy such as galileon modified gravity and others.Comment: 22 pages and 7 figures, minor clarifications added, revised version to appear in PR

Asymptotic cosmological regimes in scalar–torsion gravity with a perfect fluid

© 2016, The Author(s).We consider the cosmological dynamics of a nonminimally coupled scalar field in scalar–torsion gravity in the presence of hydrodynamical matter. The potential of the scalar field have been chosen as power law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker, and tracker solutions and study the conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of the regimes studied in the present paper is stable to the future

Dynamical features of scalar-torsion theories

© 2015 American Physical Society. 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

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 02. 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

© 2014 American Physical Society. 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

Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields

© 2016 IOP Publishing Ltd and Sissa Medialab srl.We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant

Mutated hybrid inflation in f(R,□R)f(R,{\Box}R)-gravity

A new hybrid inflationary scenario in the context of $f(R,{\Box}R)$-gravity is proposed. Demanding the waterfall field to 'support the potential from below' [unlike the original proposal by Stewart in Phys. Lett. B345, 414 (1995)], we demonstrate that the scalar potential is similar to that of the large-field chaotic inflation model proposed by Linde in Phys. Lett. B129, 177 (1983). Inflationary observables are used to constrain the parameter space of our model; in the process, an interesting limit on the number of e-folds N is found.Comment: 9 pages, 2 figures, LaTeX2e, v2: Sec.3 expanded and improved, 1 Fig. added, a new result included, some Eqs. corrected, 2 References adde

Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term

We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $\Phi(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $\Phi$.Comment: published version, references update

Cosmological dynamics in six-order gravity

We consider cosmological dynamics in generalized modified gravity theory with the $R\Box R$ term added to the action of the form $R+R^N$. Influence of $R \Box R$ term to the known solutions of modified gravity is described. We show that in particular case of $N=3$ these two non-Einstein terms are equally important on power-law solutions. These solutions and their stability have been studied using dynamical system approach. Some results for the case of $N \ne 3$ (including stability of de Sitter solution in the theory under investigation) have been found using other methods