Stability and bifurcation analysis of interacting f(T) cosmology

Abstract

The present work deals with dynamical system analysis of Interacting f(T) cosmology. Einstein field equations are second order non-linear differential equations. So it is very difficult to solve them analytically. We can draw the vector field and analyze the stability of the universe in different phase by dynamical system analysis. By suitable transformation of variables the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by center manifold theory. Possible bifurcation scenarios have also been explained.

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

“…From the above discussion on the bifurcation diagrams, we found the possibility of transcritical bifurcation exhibited by the system (37)- (38). In what follows, we summarize the occurrence of bifurcation and mathematically analyze the transcritical bifurcation with ξ as the bifurcation parameter using Sotomayor's theorem.…”

“…As the phase space (39) is in general not compact, for the sake of completeness, we analyze the nature of the system (37)- (38) at infinity by employing the Poincaré's projection method involving the following transformation [19]:…”

“…In this section, we shall discuss the occurrence of local bifurcation of the system (37)- (38) with respect to parameters ξ and n. Then we extract the condition on ξ and n under which the present model describes the generic evolution of the Universe. In the case of a two-dimensional system, we can completely characterize the structural stability by Peixoto's theorem.…”

“…It is worth mentioning that interesting bifurcation scenarios were reported in the Randall-Sundrum braneworld model [33], interacting Veneziano ghost DE [34], Brans-Dicke model [35], nonminimal coupled scalar field model [31,36] etc. Recently, bifurcation scenarios and chaos were discussed in the context of Hořava-Lifshitz gravity [37], non-minimal coupled scalar field with Ratra-Peebles potential [21], interacting f (T ) gravity [38] and bulk viscous cosmology [39]. These recent work show that the study of bifurcation is important in cosmology, giving rise to interesting scenarios.…”

Dynamics in varying vacuum Finsler–Randers cosmology

“…Thus for a healthy theory to be viable, the critical point analysis should provide points where the universe will be accelerating and also these points to be stable. This analysis has been applied in various cosmological models, for instance see and references therein [130,131,[135][136][137][138][139][140][141][142][143][144][145][146][147] .…”