Classes of nonminimally coupled scalar fields in spatially curved FRW spacetimes

Abstract

In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant, i.e. we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation.

Cosmological dynamics and bifurcation analysis of the general non-minimal coupled scalar field models

“…As expected, the above quantities (11) and (12) reduce to the familiar relative energy densities of a scalar field and matter for the minimal coupled case (i.e., F(φ) = 1) respectively. Further, the quantity (11) reduces to the relative energy density of the cosmological constant for a non-dynamical scalar field (i.e., the GR case).…”

“…One can also predict the sensitivity of the solution to initial conditions. Dynamical system methods have been used extensively in cosmology; see [3][4][5][6][7][8][9][10][11][12][13][14][15] for relevant work and [16] for a comprehensive review.…”

“…In most of the dynamical analysis for the non-minimal coupled scalar field models, the dynamical variables are constructed for a specific case of coupling or potential functions in flat or curved spacetime [12,[24][25][26][27][28][29][30][31]. However, the analysis for a general non-minimal coupled scalar field model will certainly help us to identify classes of viable models.…”

Global portraits of nonminimal inflation

“…Yet, in that approach the dynamical system does not immediately close for an arbitrary potential, and one typically needs to resort to supplementary quantities or variables which complicates the situation. Many authors prefer to work directly on the (φ, φ) plane [35][36][37][38][39][40][41][42][43][44][45][46][47] which can be made compact using Poincaré transformation. However, this choice leads to visual difficulties for the following reason.…”

Dynamical description of a quintom cosmological model nonminimally coupled with gravity

“…In scalar tensor theories of gravitation the addition of non-minimal couplings with gravity represent a viable direction supported by different hypothetical models [69][70][71][72][73][74]. The effects of the non-minimal couplings with gravity have been investigated in single scalar field theories [75][76][77][78], by considering the linear stability theory, showing the viability of the corresponding models [79][80][81][82][83][84][85][86]. Furthermore, in scalar tensor theories based on teleparallel gravity the models non-minimally coupled with gravity are constructed by using the corresponding analogous invariant scalars, the torsion [87] and boundary coupling [88] parameters.…”