Quintessence scalar field: A dynamical systems study

Abstract

The present work deals with a dynamical systems study of quintessence potentials leading to the present accelerated expansion of the universe. The principal interest is to check for late time attractors which give an accelerated expansion for the universe. Two examples are worked out, namely the exponential and the power-law potentials.

Observational constraints on the extended Chaplygin gas inflation

“…It is also possible to study interacting case of these models (Khurshudyan et al 2014c(Khurshudyan et al , 2014dRoy and Banerjee 2014). Hence, the Hubble parameter can written as follow,…”

Stability analysis of a holographic dark energy model

“…For a particular value of λ, Eqs. (13) and (14) lead to an expression for the deceleration parameter q in terms of the scale factor a as, Fig. 1 Phase plot of the system when λ = 10 and C 2 = 0.7…”

“…However, such analysis is more frequently used where a scalar field is involved. For an inflation field, the dynamical systems study has been used by Gunzig et al [11] and Carot and Collinge [12] while Urena-Lopez [13], Roy and Banerjee [14] used it for a quintessence field. Kumar et al [15], Sen et al [16], Roy and Banerjee [17] and Fang et al [18] utilized the dynamical systems analysis for an axionic quintessence, a thawing dark energy, tracking quintessence and phantom, tachyonic and k-essence fields respectively.…”

Extended phase space analysis of interacting dark energy models in loop quantum cosmology

“…This type of generalization has been widely studied in different cosmological frameworks: e.g. standard quintessence models [50,51], braneworld theories [52][53][54], k-essence [55], chameleon theories [56], scalar-fluid theories [57] and (non-interacting) LQC [58]. In these investigations the dimension of the resulting dynamical system increases by one if compared to that of the exponential potential case, making the analysis slightly more complicated.…”