Dynamical system analysis of brane induced gravity with tachyon field

Abstract

In this manuscript we use the dynamical system approach to study the linear dynamics of a normal DGP brane-world model with a tachyon field as the dark energy component. Our focus is on a Gaussian tachyonic potential in which the parameter λ = −V φ /V 3/2 , goes to infinity. One of the most important results of this study is that we find critical submanifolds which indicate the effect of extra dimension. Also, we find that in this model the universe will experience another transition from acceleration to deceleration in the future.

The Stability Analysis of Brane Induced Gravity with Quintessence Field on the Brane with a Gaussian Potential

“…Since an expanding universe and a contracting one are independent submanifolds, we can study them separately [47], [49]. In the following, we will focus on the more popular expanding case.…”

“…Here, we are interested in studying the behavior of the model in the case of a Gaussian potential. Assuming λ, changes sufficiently slow such that we can consider it as a constant within any infinitesimal period of time during the evolution of the universe, we can regard all the critical points in TABLE I, and the ones we obtained at infinity, as the instantaneous critical points of respective dynamical system [49]- [53]. With this assumption, it is clear that CP 5 , CP 6 and CP 7 , are moving critical points which can indicate where the solution tends to at each instant if it evolves in 4D.…”

Constant-roll inflation in brane induced gravity cosmology

“…On the opposite side, the case = −1, called normal branch needs a dark energy component to explain the late-time acceleration but it is ghost free. The dynamics of the Universe in a DGP scenario has been frequently studied in the literature [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Specifically, the idea of inflation has also been investigated in the context of the basic DGP brane-world cosmology and its generalizations [66][67][68][69][70][71].…”

Dynamical System Analysis of Randall-Sundrum Model with Tachyon Field on the Brane

“…The dynamical system perspective of a self-interacting scalar field in a RSII braneworld model and also in another interesting 5D braneworld model called DGP, has been investigated in [52] and [53], respectively. Specifically, in a recent article we have studied the details of a DGP braneworld cosmology with a tachyon field on the brane using this method in [54]. In all of these articles there is at least one stable critical point that behaves as a late time attractor, in addition to some other saddle or unstable critical points that correspond to other cosmological periods.…”

“…The same work has been done in [50], for only a 4D tachyon scalar field DE scenario, but with different types of potentials. In [54], we have also studied the existence of instantaneous critical points in a tachyon DGP cosmology with a Gaussian potential.…”