Cosmological dynamics of a nonminimally coupled scalar field system and its late time cosmic relevance

Abstract

We investigate the cosmological dynamics of non-minimally coupled scalar field system described by F (φ)R coupling with F (φ) = 1 − ξφ N R(N ≥ 2) and the field potential, V (φ) = V0φ 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 GN thereby leading to a ghost dominated universe in future and a transient quintessence(phantom) phase with GN > 0 around the present epoch 1 . We also carry out comparison of the model with other competing models of dark energy such as galileon modified gravity and others.

Global stability analysis for cosmological models with nonminimally coupled scalar fields

“…Using the analysis of [19], it is possible to show that for the case of ξ < 0 (the only case we consider in the present paper) the form of phase diagrams does not depend on ξ and depends only upon relations between power indexes of the coupling function and the scalar field monomial potential. This allows us to characterize completely the global feature of cosmological dynamics in the model in question using a limiting number of phase portraits.…”

“…The models with the Ricci scalar multiplied by a function of the scalar field are being intensively studied in cosmology [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] (see also [23,24,25] and references therein). Induced gravity models, wherein the curvature arises as a quantum effect [26], and models, where both the Hilbert-Einstein term and the scalar field squared multiplied by the scalar curvature are present, have been applied to quantum cosmology [27] and are being intensively studied in the inflationary cosmology [7,8,9,10].…”

“…Note that dynamical system methods are extensively used for analysis of cosmological models with scalar fields [17,19,36,39,37,38]. Using these methods several different asymptotic regimes have been found, and their stability has been investigated for the simplest case of quadratic coupling in [36] and for other power-law coupling in [19]. However, as such analysis usually requires transition to expansion normalized variables which can be not smooth in some points, this results in the fact that some solutions can be lost in this procedure.…”

Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints

“…2(a) and in the j − s plane in Fig. 2(b) in the range −1 ≤ q < 1 by considering the mean values of the model parameters given in Table 3 from observations. For comparison, we include also some alternatives to the ΛCDM model such as the Galileon, Chaplygin Gas and DGP models (for these models see [63] and references therein) in the figures. The arrows on the curves show the direction of evolution and the dots on the curves represent the present values of the corresponding {q, j} and {j, s} pairs while the black dots show the matter dominated phases of the models.…”

Cosmological models in modified gravity theories with extended nonminimal derivative couplings

“…The nonminimal derivative coupling leads to cosmological models with rich phenomenology, such as solutions containing a Big Bang, expanding Universes with no beginning, cosmological bounces, eternally contracting Universes, a Big Crunch, and a Big Rip avoidance [33,[36][37][38][39][40][41][42]. In particular, it was shown that one is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential [32].…”