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

Abstract

In this manuscript we consider a normal branch of DGP cosmological model with a quintessence scalar field on the brane as the dark energy component. Using dynamical system approach we study the stability properties of the model. We find that λ, as one of our new dimensionless variables that is defined in terms of the quintessence potential has a crucial role in the history of the universe. We divide our discussion into two parts: a constant λ, and a varying λ. In the case of a varying λ, which is the main part of this work, we consider a Gaussian potential for which λ goes to infinity, asymptotically. Here, all the critical points which were obtained in the case of a constant λ, can be assumed as instantaneous critical points. We discuss the evolution of dynamical variables in such a model and conclude that their asymptotic behaviors follow the trajectories of the moving critical points. Also, we find two different possible fates for the universe. In one of them it experiences an accelerated expansion, then enters a decelerating phase and finally reachs a stable matter dominated solution. In the other scenario, the universe approaches the matter dominated critical point without experiencing any accelerating expansion.

Physical properties of a quintessence anisotropic stellar model in f(Q) gravity and the mass–radius relation

“…To investigate the solution of compact stars in f (Q) gravity, the quintessence field is used in the energy-momentum tensor, in particular. A quintessence scalar field on the brane was taken into account by Ravanpak [36] as the dark energy component of a normal branch of the Dvali-Gabadadze-Porrati (DGP) cosmological model. They investigate the stability characteristics of the model using the dynamical system technique and discover that λ, one of their new dimensionless variables that are specified in terms of the quintessence potential, plays a significant role in the development of the universe.…”